Area under a curve Area enclosed by a curve No Answers Chosen No Answers Chosen Rectangular Coordinates Polar Coordinates No Answers Chosen No Answers Chosen Area of a sector Length of Curve No Answers Chosen No Answers Chosen Possible answers

Q: 3 The line y = -x passes through the origin in the x, y-plane. What is the measure of the angle (in…

A: NOTE: You have posted multiple questions, we have given answers to the first question, if there is a…

Q: A large metal disk with radius of 1 m has been made. The density of the metal disk is given by p(z,…

A: Given A large metal disk with radius of 1m has been made i.e. r=1 and ρx,y=2+6xy and θ=0 to θ=π3

Q: The curve y = 9/x is rotated about the x- axis between x = 0 and x = 1 through an angle of 2r…

A: If  the curve   is rotated about x-axis then the surface area of the solid obtained is given by…

Q: %3D s { sinat I E cas at } = S fis) %3D the method Find &coset by using Homework = %3D

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Q: The path of a projectile is modeled by the parametric equations                        x = (90 cos…

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Q: a). We can use the equation of a curve in polar coordinates to compute some areas bounded by such…

A: (a) Given that the equation of a curve in polar coordinates to compute some areas bounded by…

Q: Find the points of horizontal tangency to the polar curve. r = a sin θ      0 ≤ θ < π, a > 0…

A: Calculation:The polar curve is r = a sin θ, where 0 ≤ θ < π and a > 0.In order to find the…

Q: [SADT] The parametric equations for the motion of a charged particle released from rest in electric…

A: In this question, concept of derivative is applied. Derivative The derivative expresses the rate of…

Q: polar curves. 63. The complete circle r = a sin 0, where a > 0

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Q: Arc length of polar curves Find the length of the following polar curves. The spiral r = eθ, for 0 ≤…

A: Given polar curve isr=eθ for 0≤θ≤2πn when n is positive integer Formula used :-arc length…

Q: A large metal disk with radius of 3 m has been made. The density of the metal disk is given by p(x,…

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Q: The figure shows a device that can be used to measure the speed of a bullet. The device consists of…

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Q: Find the area of the region. Three petals of r = cos(90)

A: Given: The region is three petals of r=cos9θ. Formula for area in polar cordinates: A=12∫βαfθ2dθ and…

Q: A right circular cone with dimensions (R, h) as shown in figure is rolled about the Z-axis keeping…

A: Given: R = Radius of the cone, 9cmh  = Height of the cone, 12cmP = Perimeter of the base of the…

Q: The curves 71(t) =(-t, t°, 2t³) and 72(t) = (sin(– 4t), sin(5t), t – m) intersect at the %3D origin.…

A: Angle between two curves at point of intersection is the angle between their tangent vectors at that…

Q: 3. Find the area of the region inside the circler-3 sine and outside the limacon r= 2 - sine. Sketch…

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Q: Find the area enclosed by the polar curve r = 3cose. Find the area common between the curves r= a (1…

A: First Part: Given function is r=3cosθ Since is an asymmetric function so the area formed under it…

Q: Angle of tangent to curve 8 of 13 Review Constants Part A What angle does the tangent to the curve…

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Q: 8. Water flows into a vertical cylindrical tank at 12 ft /min; the surface rises in 6 in/min. Find…

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Q: What is the area enclosed by the curve r = 2 cos 30? Answer is in square units. Use two (2) decimal…

A: First draw the diagram then find the interval and last intergate it.

Q: a) First make a cartesian graph ofr as a function of 0, and then, using this, carefully plot the…

A: Use Area in polar form.

Q: Given r = 2(1-sin theta)  1. Find the tangent line equation at (r, theta) = (2, 0). Show all work to…

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Q: Point P sweeps out central angle 0 as it rotates on a circle of radiusr as given below. Find the…

A: We know that,

Q: Calculate the length of the polar curve r =1- sin Oon the given interval [0,2n]

A: Given: r=1-sin θInterval 0, 2π

Q: Arc length of polar curves Find the approximate length of the following curve. The limaçon r = 3 - 6…

A: Consider the following curve: r=3-6cosθ

Q: . Let C1 and C2 be two curves in polar coordinates, whose equations are given by: (see attached…

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Q: The parametric equations x = 1-6 sin 3t and y = 4 + 6 cos 3t for 0 sts /2 represent a curve C. Draw…

A: Here we have, x=1-6sin(3t) and y=4+6cos(3t) for 0≤t≤π2 represent a curve C.

Q: Find the area of the surface formed by revolving the polar equation over the given interval about…

A: Given:r=6 cosθInterval: 0≤θ≤π2S=2π∫αβ r sinθ r2+drdθ2  dθ

Q: 2.1 6. Diagram not to scale The above diagram shows a sector with radius 6 subtending an angle of…

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Q: Find the area of the surface formed by revolving the polar equation over the given interval about…

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Q: Write an integral that represents the area of the shaded region of the figure. Do not evaluate the…

A: Form the graph it is observed that the area is required only for the right half of the circle.…

Q: Find the area of the region enclosed by the inner loop of the curve. r = 6 + 12 sin(0)

A: Given  r=6+12sin(θ) 0=6+12sin(θ)-6=12sin(θ)-12=sin(θ) sin is negative in third and fourth quadrant…

Q: 76. A small plane flies in a sinusoidal pattern at a constant altitude over a river. The path of the…

A: Find distance

Q: on equations between rectangular and polar coordinates are as follows (th x = r cos 0, y=r sin 0 p2…

A: Pythagoras theorem states that the square of the hypotenuse is equal to the sum of the squares of…

Q: Find the area of the shaded region, where the polar curve is given by r = 1+sin(0). You may need to…

A: Given that the polar curve is r=1+sinθ.

Q: Average temperature on a sphere The temperature on the surface of asphere of radius a varies with…

A: We are given function T as follows: The average temperature is given by:

Q: 6. a) On polar graph paper, sketch the cuve given by r = 2 sin(0). b) Find 2 and explain how you…

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Q: Q3: What symmetries do this curve have?? r = 1+ sin? 0 Q4: Find the length of the curve r = 4 – 4…

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Q: Find the length of the polar curve. r= sine, 0<0SI Solve by hand. No calculator. Show all work.

A: Given:- r=sin(ϴ) , 0≤ϴ≤π To find:- Length of given polar  curve   over interval 0≤ϴ≤π

Q: Convert (x2 + y²)² = x² -y² to polar coordinates and calculate the exact area enclosed by the…

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Q: Find the area of the region inside r = 9 cos 0 and inside the rose curve r = 9 sin 0 Note: a.…

A: 1st we will find values of r and θ and also intersecting points  to trace the curves . Then shade…

Q: 9. Find the area of the region inside the cardioid r= 2-2 cos(0) and outside the circle r= 2. Then…

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Q: Arc length of polar curves Find the length of the following polar curves. The complete limaçon r = 4…

A: Given: Polar curve is r=4-2cosθ.

Q: Find the area of the surface formed by revolving the polar equation over the given interval about…

A: Consider the following polar equation: r=2sinθ Differentiate r with respect to θ:…

Q: Find the slope of the line tangent to the polar curve at the given points. r= 3 cos 20; at the tips…

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Q: Arc length of polar curves Find the length of the following polar curves. The spiral r = 4θ2, for 0…

A: Given that, r = 4θ2 Where 0 ≤ θ ≤ 6 Differentiating with respect to θ we get, dr/dθ = 8θ

Q: 3. A section of highway has vertical and horizontal curves with the same design speed. A vertical…

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Q: 6. Sketch the graph of the cardioid r =1+ sine and the circle r= 3sine. Shade the region that is…

A: Given,  Two  curves  Cardioid -  r=1+sin(θ)   Circle -r= 3sin(θ) Graph:

Q: Arc length of polar curves Find the approximate length of the following curve. The limaçon r = 3 + 2…

A: Consider the provided curve, r=3+2 cosθ Find the approximate length of the polar curve. We can write…

Q: 7. Translate the polar equation into rectangular coordinates and graph it. Set up and evaluate the…

A: Use polar equation into simple equation

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.