Arc Length Formula

The length traveled along the arc = (0. Find the length of the curve defined by the vector-valued function $\vec{r}(t) = \sqrt{2}t \vec{i} + e^t \vec{j} + e^{-t} \vec{k}$ for $0 ≤ t ≤ 1$. But since there's only a few ways to contrive these problems so that the algebra (and ensuing …. In relation to the two arc length formulas seen on this page, both show that arc length, s, is expressed as "some value" times the radius, r. Once you know the radius, you have the lengths of two of the parts of the sector. Now, we can apply the formula for finding the length of an arc if the angle is given in Area and Arc Length of a Sector Tutoring and Learning Centre, George Brown. Enter central angle =63. Intercepted arc: Corresponding to an angle, this is the portion of the circle that lies in the interior of the angle together with the endpoints of the arc. Please enter any two values and leave the values to be calculated blank. 816mm, Bend Angle 90degrees. Similarly, if there is a limit, you cannot calculate length across that limit. 2 ), there is a number ti in (xi,xi+1) such that f′ (ti)Δx=f (xi+1)−f (xi), so the length of the line segment can be written as √ (Δx)2+ (f′ (ti))2Δx2=√1+ (f′ (ti))2Δx. Suppose that the helix r(t)=<3cos(t),3sin(t),0. Can calculate area, arc length,chord length, height and perimeter of circular segment by radius and angle. If the circumference of the circle is 96, what is the length of minor arc LN? In the figure above, point O is the center of the circle, line segments LM and MN are tangent to the circle at points L and N, respectively, and the segments intersect at point M as shown. 6 then click the "DEGREES" button. The ArcLength of a curve in Cartesian coordinates is. With hand-held SB-800 on SC-29 cable, TTL|BL flash setting. Improve your math knowledge with free questions in "Arc length" and thousands of other math skills. We will assume that f is continuous and di erentiable on the. Arc Length in Polar Coordinates. Arc Length is the length of the arc that is part of the circumference. Be careful!! Units count. What is the arc length of sqrt(2-x^2) - Calc II question? Use the arc length formula to find the length L of the curve below, 0 ≤ x ≤ 1. Formulas for right triangles. The general formulas for calculating the arc length of a section of a circle are: s = 2πr(θ/360), when θ is measured in degrees, and: s = rθ, when θ is measured in radians; Where s is the arc length and r is the. For examples can be found on the Arc Length of Curves in Three-Dimensional Space Examples 2 page. 433mm, Arc length 0. Therefore, you get the formula [math]L=r\theta[/math]. 8 then click "CALCULATE" and your answer is Arc Length = 4. Let specify the discretization interval of the line segments, and denote the total length of the line segments by. rectangle = 2a + 2b triangle = a + b + c. The arc length of f between a and b is s = Z b a q 1+[f0(x)]2 dx Similarly, for a smooth curve given by x = g(y), the arc length of g between c and d is s = Z d c q 1+[g0(y)]2 dy. The observer at O is a height H obs above A. If you want to continue on from there and calculate the time required to travel the arc, simply divide the distance by the ground speed. You can quickly measure the arc length using a string. 1 The arc length of the Archimedean spiral The Archimedean spiral is given by the formula r= a+b in polar coordinates, or in Cartesian coordinates:. Other lengths may be used—such as 30 metres or 100 metres where SI is favoured, or a shorter length for sharper curves. Determining the length of an irregular arc segment is also called rectification of a curve. Figure not drawn to scale. Now we're going to determine a formula for the arc length of a smooth parametric curve x = f ( t ), y = g ( t ), using the parametric functions f and g, so that we don't have to first find the corresponding Cartesian function y = F ( x) or equation G ( x, y) = 0. To do this, set up an integral over the parameter. When constructing them, we frequently know the width and height of the arc and need to know the radius. Arc Length and Sector Area I. 1416 x Diameter: Arc Length: 0. In this section, we study analogous formulas for area and arc length in the polar coordinate system. Then we will apply the formula to some of the questions below. Arc Length Formula For Degrees. If you want to learn how to calculate the arc length in radians, keep reading the article!. Thus the task is to nd the antiderivative of p 1 + x2. 5 × 2π = 15π = 47. Define the integrand as an anonymous function. Work out the arc length of this sector: The angle inside the sector is 134⁰, so x = 134⁰. Stewart 10. Arc Length and Area of a Sector To find the length of arc AB, we convert to radians by multiplying by /180. Thus, the length of the arc AB will be 5/18 of the circumference of the circle, which equals 2 πr, according to the formula for circumference. I need some help from the math types out there for writing a formula for arc length. Arc Measure given in Radians. square = 4a. An arc is a particular portion of the circumference of the circle cut into an arc, just like a cake piece. Arc length is the distance between two points along a section of a curve. The meridian arc length from the equator to arbitrary latitude is of utmost importance in map projection, particularly in the Gauss-Krüger projection. In this article, we explain the arc length formula in detail and provide you with a step-by-step instruction of how to find the arc length. Arc Length of a Curve. 1 The Length of a Pulley Belt To calculate the length of a pulley belt that wraps around two pulleys we need to compute the length of pulley common tangents, both the outside tangents and the tangents that pass between the pulleys in the case of a crossed belt. When you use arc length as the parameter, the ending value is always the length of the curve. When the central angle is in radians, the arc length formula is: Arc length = r. Hold down the Ctrl key as you drag to draw in a clockwise direction. The line integrals in equation 5. Remember that the arc will be cut into the portion of a board between whatever material is reserved for jointery. The concept of angular displacement and arc length are demonstrated. Geometry calculator solving for circle arc length given radius and central angle. Since this format always works, it can be turned into a formula: Distance Formula: Given the two points ( x 1 , y 1 ) and ( x 2 , y 2 ) , the distance d between these points is given by the formula:. Learn arc length (formula) with free interactive flashcards. Let’s take some examplesIf radius of circle is 5 cm, and length of arc is 12 cm. In this interval, the object rotates through an angle , and traces out a circular arc of length. 2213) Results: Radius: 469. Centimeters = Inches x 2. The 8'7" arc length you show is rounded. r indicates the radius of the arc. Because of this we also refer to s as arc length. Because the rocket may wind. The main length formula Example Find the arc-length of the curve y = x3/2, for x ∈ [0,4]. So, how to get the arc length? The general formula for this is: This can be used to determine the length of any curve, even complex ones. Explanation: Arc length of a curve f(x) is given by the formula s=∫x1 x0√1+f'(x)2dx. Similarly, the arc length of this curve is given by L = ∫ a b 1 + (f ′ (x)) 2 d x. feet, Radius = feet, arc length, Sector Each arc length sector is rounded off. Then, the arc length is a function of x. Let’s derive a formula for the length L of the curve on the interval, called the arc length over [a;b]. The length traveled along the arc = (0. The arc length formula is used to find the length of an arc of a circle. Measured in degrees. 47 nautical miles. Thus the angle formed by the two tangents and the degree measure of the first minor intercepted arc also add to 180º Two Secants: ∠ CAE is formed by two secants intersecting outside of circle O. To unlock this lesson you must be a Study. The above parametrization is used conventionally, because it turns out to be numerically superior to the complementary one which would make q small near the sharper apex. And in doing so, we will develop the Arc Length Formula for integration as well as the Arc Length Function, where we can find the length of a curve from a specified starting point to any point on the curve. The observer at O is a height H obs above A. Bibtex entry for this abstract Preferred format for this abstract (see Preferences ). I build curves for wood molding. Download Citation on ResearchGate | A representation formula for curves in C3 with preset infinitesimal arc length | We consider an algebraic representation formula for meromorphic curves in C-3. So finally, here’s the formula you’ve been waiting for. p 1 + 9x4dxcomputes the arc length. s 1 + dy dx. Math Help Forum. Try some other central angle measurements. Calculating the length of an arc Hey guys, Im putting together a spreadsheet for work, and finding the length of an arc is something we often need to calculate. Step 1: The area of a rectangle is given by the formula length × width. The formula is $$ S = r \theta $$ where s represents the arc length, $$ S = r \theta$$ represents the central angle in radians and r is the length of the radius. b is not specified, ArcLengthTutor uses a default interval. The length of an arc is found by forming a ratio of the arc to the whole circle, then multiplying it by the formula for circumference, either 2 π r or π d, like this:. --- B --- * BASE () System variable Contains the table address of the screen assigned on VRAM. 4 Arc Length and Surfaces of Revolution 477 Because the definition of arc length can be applied to a linear function, you can check to see that this new definition agrees with the standard Distance Formula for the. This kind of mental activities suggests to some scientific observers that consciousness may exist in addition to the corporeal form. Arc Length of a Curve. Answer -s TT* In a given circle described below, find the missing parts. << Prev Next >>. The arc furnace equivalent circuit is very simple: X is the circuit reactance, V is the voltage without load, Va is the arc voltage and I is the current. The arc length of the curve is found by using the integrand. The arc length can be calculated using the Bend Angle (BA) and the Inside Radius (IR) using the following formula:. Equivalently, this will be the arc length of the curve parametrized by ${\bf r}(t), \, a \le t \le b\,. The length of arc is equal to radius multiplied by the central angle (in radians). - Compound miter - Saw settings for cutting molding on various wall angles and molding slopes. Just because the curve traces out \(n\) times does not mean that the arc length formula will give us \(n\) times the actual length of the curve! Before moving on to the next section let's notice that we can put the arc length formula derived in this section into the same form that we had when we first looked at arc length. Includes full solutions and score reporting. This expression for the parabola arc length becomes especially when the arc is extended from the apex to the end point (1 2 ⁢ a, 1 4 ⁢ a) of the parametre, i. The arc length of the curve is found by using the integrand. Formula The following is the calculation formula for the length of the hypotenuse of a right-angled triangle, based on the Pythagorean theorem: where c is the length of the hypotenuse, and a and b are the lengths of the other two sides. Can someone please help me write down all the formulas which are NOT included in the formula book which we need to know for the Edexcel C2 exam. Theres plenty of webpages that I can just punch the numbers in, but Id like to have it in a spreadsheet, as there are factors prior to this that have already been calculated. The Complete Circular Arc Calculator This calculator calculates for the radius, length, width or chord, height or sagitta, apothem, angle, and area of an arc or circle segment given any two inputs. Download Citation on ResearchGate | A representation formula for curves in C3 with preset infinitesimal arc length | We consider an algebraic representation formula for meromorphic curves in C-3. But since there's only a few ways to contrive these problems so that the algebra (and ensuing …. Since in any circle the same ratio of arc to radius determines a unique central angle, then for theoretical work we often use the unit circle, which is a circle of radius 1: r = 1. Find arc length. Create a formula for finding the area of a sector with any. The formula for the area of a sector of a circle (shown in red here) is derived in your textbook. " And in particular, we need to understand how to calculate arc length. An arc is a part of the circumference of a circle. I have several formulas for calculating radius and springback. Arc length of a curve can be found using the following ways:. We recently looked at some examples of parameterizing various curves in $\mathbb{R}^3$ on the Parameterization of Curves in Three-Dimensional Space page. Perimeter Formulas The perimeter of any polygon is the sum of the lengths of all the sides. $\endgroup$ - Jyrki Lahtonen Jul 1 '13 at 21:54. For any parameterization, there is an integral formula to compute the length of the curve. To give the same curve, you need to give the specific domain of the new parameter. Make sure you don't mix up arc length with the measure of an arc which is the degree size of its central angle. Figure 2 shows a graph of this arc length function for −120 ≤ D ≤ 30. When the central angle is in radians, the arc length formula is: Arc length = r. The Arc Length of a Parabola Let us calculate the length of the parabolic arc y = x2; 0 x a. Worksheet to calculate arc length and area of a sector (degrees). The working efficiency of the designed electric mode. (Radius = r, angle = theta) r * theta = arc length doesn't work here. The formula is $$ S = r \theta $$ where s represents the arc length, $$ S = r \theta$$ represents the central angle in radians and r is the length of the radius. Numerous branches of technology for example physics, psychology, astrophysics, and biology, are investigating the spirit, and each has their own particular ways of inquiry. Arc Measure given in Radians. Check your answer by noting that the curve is a line segment and calculating its length by the. The calculator will find the arc length of the explicit, polar or parametric curve on the given interval, with steps shown. 73 3 points. Arcs are drawn in a counterclockwise direction by default. Depending on the dimension the distance between two points can be found using the following formulas: The formula for calculating the distance between two points A(x a, y a) and B(x b, y b) on a plane: AB = √ (x b - x a) 2 + (y b - y a) 2. Lesson 10-2 Measuring Angles and Arcs 695 Watch Out! Arc Length The length of an arc is given in linear units, such as centimeters. For example, if you have a function with an asymptote at x = 4 on either side, you can’t use the arc length formula across the two sections. Also, this \(ds\) notation will be a nice notation for the next section as well. 45 Central Angle: 40°22'13" (enter as 40. The perimeter of a polygon is equal to the sum of the length of its sides. We will assume that fis continuous and di erentiable on the interval [a;b] and we will assume that. Use the same units for all measurements. 08079 Chord Length: 323. Arc length is useful as a parameter because when we parameterize with respect to arc length, we eliminate the role of speed in our calculation of curvature and the result is a measure that depends only on the geometry of the curve and not on the parameterization of the curve. The length of that arc is a real number x. But, with yours maybe we can solve for y and use the arc length formula. The formula. Calculate the perimeter of a semicircle of radius 1. Can anyone help me with the formula for converting from WGS 84 / UTM Zone 34N to World Geodetic System? My problem is I want to represent some properties (polygons) in some kind of a map (image). Whilst teaching a recent AutoCAD course I was asked by a boat designer how to construct / draw an arc of a specific length. Hence, an angle must correspond to an arc length of. Calculated flat-blank length = 1. To calculate the radius. Re: Arc Length Formula Please Login or Register to view this content. Suppose that the helix r(t)=<3cos(t),3sin(t),0. So, it's the square root of one plus f-prime of x squared d x. Catenary Fit In order to find a catenary that has width and height all we need to observe that is and even function and that goes through and we also want it to go through the point. For example, if you have a function with an asymptote at x = 4 on either side, you can’t use the arc length formula across the two sections. Thus the task is to nd the antiderivative of p 1 + x2. The formula for the circumference of a circle is based on the relationship between the flat surface. 4908" wrist pin hole Includes Rod Bearing Sell $83. Let's first begin by finding a general formula for computing arc length. The integrals generated by both the arc length and surface area formulas are often difficult to evaluate. AP® Calculus BC 2011 Free-Response Questions Form B. Formulas for Circumference and Area. For example, if you have a function with an asymptote at x = 4 on either side, you can't use the arc length formula across the two sections. Therefore, you get the formula [math]L=r\theta[/math]. In Japan, the previously used formula for the meridian arc length was a power series with respect to the first eccentricity squared of the earth ellipsoid, despite the fact that a more concise. Exam Style Questions Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser You may use tracing paper if needed !The arc length is 4. Arc Length Formulas. So we know that the arc length Let me write this. To give the same curve, you need to give the specific domain of the new parameter. Just because the curve traces out \(n\) times does not mean that the arc length formula will give us \(n\) times the actual length of the curve! Before moving on to the next section let's notice that we can put the arc length formula derived in this section into the same form that we had when we first looked at arc length. Arcs are drawn in a counterclockwise direction by default. The parametric arc length formula becomes Now and , so Square and add, using the fact that : Hence,. Degree/Radian Circle. 5 × 2π = 15π = 47. We see there is a minimum that Mathematica determines to be 2. So, how to get the arc length? The general formula for this is: This can be used to determine the length of any curve, even complex ones. Arc length is given by. The heavy arc OH is the ray that's horizontal at the observer; so any point on it is seen at the observer's astronomical horizon. 6 then click the "DEGREES" button. I am using objective c since I want to use a computer to display the answers. Let's go over each arc length equation step-by-step. Since an arc is a portion of a circle, its length is a fraction of the. To unlock this lesson you must be a Study. Given a function f f f that is defined and differentiable on the interval [ a , b ] [a, \, b] [ a , b ] , the length L L L of the curve y = f ( x ) y = f(x) y = f ( x ) in that interval is L. Then the vectors t, n, b are. Arc length formula is used to calculate the measure of the distance along the curved line making up the arc (segment of a circle). We deliver steam as if your life depends on it. Can someone please help me write down all the formulas which are NOT included in the formula book which we need to know for the Edexcel C2 exam. Geometry calculator solving for circle central angle given arc length and radius. Issue with a school project, while loop! These cups are made from a circular waxed paper 4 inches in radius by removing a sector of length x. The length of a curve or line. Find the approximate length of an arc of this circle, if the length of the chord of the arc is 3 feet also. 73 3 points. Radians, like degrees, are a way of measuring angles. An arc is a part of the circumference of a circle. An arc length is a portion of the circumference of a circle. The distance along the arc (part of the circumference of a circle, or of any curve). Together we will walk through several examples, and utilize our integration techniques, namely U-Substitution, to find the length of the curve. Mathematics is concerned with numbers, data, quantity, structure, space, models, and change. Can someone please help me write down all the formulas which are NOT included in the formula book which we need to know for the Edexcel C2 exam. The figure below gives the relationship between degrees and radians for the most common angles in the unit circle measured in the. Therefore, above theorem gives a simple formula to determine the ‘‘arc length of given Elliptical arc segment lying within a quadrant of the ellipse ’’, in the same manner, it is meant for other elliptical functions. Henceforth we assume that α : I → R3 is a regular curve parameterized by arc length. For example, if you have a function with an asymptote at x = 4 on either side, you can’t use the arc length formula across the two sections. Hold down the Ctrl key as you drag to draw in a clockwise direction. Can calculate area, arc length,chord length, height and perimeter of circular segment by radius and angle. In a general coordinate chart, the ArcLength of a parametric curve is given by , where is the metric. I build curves for wood molding. Arc Length Evaluate the unknown variable. Then β is also parametrized by arc length and α and β have the same curvature. Therefore, there is a direct relationship between arc length and x & y length for each triangle. Regard as the parameter. To develop the blank flat length for a cylinder rolled from sheet or plate is quite simple: Essentially, you should calculate the centerline arc: (Outside Diameter – Thickness) x 3. Arc length of a circle is the distance measured as the length. Find the length of an arc that subtends [forms] a central angle of 2 rad in a circle. Formulas for Circumference and Area. Introduction. all in inches, all in cm, etc. The length of the arc for this scenario can be calculated as: Where R' is the radius of the arc on the neutral axis. A one-dimensional region can be embedded in any dimension greater than or equal to one. Let us consider a circle with radius rArc is a portion of the circle. The arc length is the length of the crust on the piece of pizza you get. Find the radius ® of that circle. The arc length formula can be re-written in polar coordinates too. Step 2: So, the area of the rectangle 13 cm long and 9 cm wide is 13 × 9 = 117 square cm. edu Our Approach What is an Ellipse? The equation for an Ellipse Polar Our Problem Finding the arc length of an ellipse Rectangular Finding the arc length of an Ellipse Right. Similarly, if there is a limit, you cannot calculate length across that limit. More precisely, when \ t!000, we get (ds)2 = (dx)2 + (dy)2: The di erential dsis called the arc length element, or the Riemannian metric, of R2. Note: the integral also works with respect to y, useful if we happen to know x=g(y):. is arc voltage and current, U. - Arcs - Calculates arc length, radius, angle in rads and degrees. The general formulas for calculating the arc length of a section of a circle are: s = 2πr(θ/360), when θ is measured in degrees, and: s = rθ, when θ is measured in radians; Where s is the arc length and r is the. Before laying out your arc be sure to mark off the portions of your piece used for jointing. Let us consider a circle with radius rArc is a portion of the circle. It may be necessary to use a computer or calculator to approximate the values of the integrals. Arc Length Formula (s) Using the first ds will require x limits of integration and using the second ds will require y limits of integration. Central Angle of a Circle Formula. often leads to integrals that cannot be evaluated by using the Fundamental Theorem, that is, by finding an explicit formula for an indefinite integral. In this case, the function, y = F(x) has been replaced by the polar function r(θ). Then, the arc length is a function of x. In other words, it’s the distance from one point on the edge of a circle to another, or just a portion of the circumference. not the inside edge. Arc Length Arc length is the distance between the endpoints along an arc measured in linear units. Math Help Forum. Arc length = (Ө/360˚)2πr, Ө is given in degrees. This is often done by setting x = sinht or x. Note that I have modified the definitions of a and b. Let's derive a formula for the length $L$ of the curve on the interval, called the arc. Work out the arc length of this sector: The angle inside the sector is 134⁰, so x = 134⁰. Just because the curve traces out \(n\) times does not mean that the arc length formula will give us \(n\) times the actual length of the curve! Before moving on to the next section let's notice that we can put the arc length formula derived in this section into the same form that we had when we first looked at arc length. Let’s derive a formula for the length L of the curve on the interval, called the arc length over [a;b]. Each line that contains the section will be the same length, as the center of a circle extends to the same length when you get to the end of the circle. Then we apply the formula s = r. L Total Length of any circular curve measured along its arc Lc Length between any two points on a circular curve R Radius of a circular curve ∆ Total intersection (or central) angle between back and forward tangents. Nikon D70 with 12-24mm f/4G ED-IF AF-S DX Nikkor @ 12mm, f/7. 4 Length of a Plane Curve Arc Length Formula If y = f(x) is a smooth curve on the interval [a;b]; then the arc length L of this curve over [a;b] is de ned as L = Z. Again, when working with π, if we want an exact answer, we use π. The arc length is the length of the crust on the piece of pizza you get. To calculate compression height:subtract deck height - (stroke divided by 2) - rod length. Enter central angle =63. Show Instructions In general, you can skip the multiplication sign, so `5x` is equivalent to `5*x`. I need some help from the math types out there for writing a formula for arc length. You can use the measure of the arc (in degrees) to fi nd its length (in linear units). The curve traced by. It's usually less. Click to place the dimension line. Learn arc length (formula) with free interactive flashcards. ' and find homework help for other Math questions at eNotes. When you use arc length as the parameter, the ending value is always the length of the curve. The length of an arc can be found by one of the formulas below for any differentiable curve defined by rectangular, polar, or parametric equations. ANGLE AND SEGMENTS IN CIRCLES, ARC LENGTH AND SECTOR AREA: We will / I will be able to determine the measures of central angles and inscribed angles of a circle, make conclusions about the angles of a quadrilateral inscribed in a circle, justify and use the formulas for the circumference and area of a circle, determine relationships between segments in a circle and angles formed by lines that. Set up the formula for arc length. Lesson 10-2 Measuring Angles and Arcs 695 Watch Out! Arc Length The length of an arc is given in linear units, such as centimeters. Now we need to find out the r when we know the arc angle = 48 o and arc length as 16 cm. Answer -s TT* In a given circle described below, find the missing parts. , for the full cone r1 is zero. For instance, 47. For a large radius this point, sometimes called the K factor is closer to the middle of the metal thickness. The curve traced by. The arc length is longer than the straight line distance between its end points. Another way to interpret the final equation is to say that the square root term represents the length of the hypotenuse of a triangle with. Arc Length Formula For Degrees. The first example illustrates a sequence of polygonal approximations of a rectifiable curve, i. ANGLE AND SEGMENTS IN CIRCLES, ARC LENGTH AND SECTOR AREA: We will / I will be able to determine the measures of central angles and inscribed angles of a circle, make conclusions about the angles of a quadrilateral inscribed in a circle, justify and use the formulas for the circumference and area of a circle, determine relationships between segments in a circle and angles formed by lines that. Determining the length of an irregular arc segment—also called rectification of a curve—was historically difficult. The above parametrization is used conventionally, because it turns out to be numerically superior to the complementary one which would make q small near the sharper apex. Radian measure and arc length can be applied to the study of circular motion. But sometimes we need to work with just a portion of a circle's revolution, or with many revolutions of the circle. OwlCalculator. Arc length is given by. Where is in radians. The students can use the formulas as an entry point to the problem. Formula for $$ S = r \theta $$ The picture below illustrates the relationship between the radius, and the central angle in radians. 1 The arc length of the Archimedean spiral The Archimedean spiral is given by the formula r= a+b in polar coordinates, or in Cartesian coordinates:. A = (Θ ÷ 360) x (D x π). When you use arc length as the parameter, the ending value is always the length of the curve. L Total Length of any circular curve measured along its arc Lc Length between any two points on a circular curve R Radius of a circular curve ∆ Total intersection (or central) angle between back and forward tangents. AUTO [[, ]] Command Produces line numbers automatically. Standing Assumption. Click to place the dimension line. The formulas I have involve the degree of angle. Describe a formula that. That is, we can create a function s(t) that measures how far we've traveled from ~r(a. The formula for the area of a sector of a circle (shown in red here) is derived in your textbook. the fundamental arc-length formula. Formulas for the area and arc length in. A one-dimensional region can be embedded in any dimension greater than or equal to one. 9 and a central angle of 1. Area of a Sector Formula. We start with f (x) = x3/2 ⇒ f 0(x) = 3 2 x1/2 ⇒ f 0(x) 2 = 9 4 x.