01: Find the angle () between the tangents lines of the 4(1 + cos 0) at the line r 3 sec 0 and the cardioid r = = points of the intersection ?

Q: 3. What is the length of the curve r = cos3 (-) where 0 < 0 <: sos

A: See the attachment

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Q: The intersection points between the curves r = 3. and r = are 1-cos e 1+cose

A: The given curves are, r=11-cosθ                      ........(1) r=31+cosθ…

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A: The parametrized curve x=e-sinθ and y=ecosθ for 0≤θ&lt;2π.

Q: 4. Find the acute angle between the curves y = sin r and y = cos r (0 < r <) at their point of…

A: We find the point of intersection by setting them equal

Q: Find the length of the curve over the given interval. r = 8(1 + cos θ), [0, π/ 3]

A: Given: To find:  The length of the curve over the given interval.

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Q: 1- Find all of the points where the curve r = 2 cos (-) intersects the circle of 3, radius v2…

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Q: Q4) The standard formula for the tangent of the sum of two angles is tan x + tan y tan(x +y) 1- tan…

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A: In this question, concept of tangent plane at any point is applied. Tangent Plane Naturally, it…

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A: We have given circles equation r=3cosu and r=sinu For intersection point of these circles…

Q: Find all angles between 0 and 2T satisfying the condition COS X = 2 Separate your answers with…

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Q: 01: Find the angle () between the tangents lines of the 3 sec 0 and the cardioid r 4(1+ cos 0) at…

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Q: Q1: show that1) d/dz [cosz] = -sin z, 2) 1+tan2 z = sec2 z

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Q: Find the area bounded by the trigonometric curves O2.828 square units 1.414 square units 3.667…

A: To find: To find the area bounded by the trigonometric curves- y=sin x and y=cos x from x=π4 to…

Q: Find the residues of sin(2²) at z = 0 and z = π. (sin z)2

A: To find the residue of sinz2sinz2 at z=0 and z=π Let  fz=sinz2sinz2=sinz2csc2z…

Q: Sketch the curve corresponding to r = 1 + cos θ.

A: we have to sketch the graph of the polar curve r=1+cos θ.

Q: find the length of the part of the r=2(1+ cosa) curve that remaîns în the r =211+ Sind) curve %3D…

A: We have to find the length of the part of the r = 2(1+cos alpha) curve that remains in the r =…

Q: 01: Find the angle () between the tangents lines of the line r = 3 sec 0 and the cardioid r 4(1 +…

A: The given question can be solved as shown in step2.

Q: Given the cardioid r= 3(1+cosθ) 0 ≤ θ ≤ 2π Determine in wich points the cardiod has vertical…

A: Differentiate the equations r=31+cosθ and x=rcosθ with respect to θ, to find drdθ and dxdθ.…

Q: Find the points on the interval -n SOSnat which the cardioid r = 1 - cos(0) has a vertical or…

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Q: Q1: show that1) d/dz [cosz] = -sin z , 2) * 1+tan2 z = sec2 z

A: In both solutions i have used the definition

Q: Find the lengths of the curves The cardioid r = 1 + cos θ

A: Given:r=1+cosθl=∫r2+drdθ2 dθ

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A:

Q: Calculate F-dr in the case when F(z,y) = (7y - sin (y) + 8)i+ (72 -e cos (y))jis conservative, and A…

A: Given that: F=7y−exsiny+8i+7x−excosyj and, rt=2tsinπt2i−π2sinπt2j for 0≤t≤1

Q: Let t be the angle between 0 and such that sin t Then cos t sin(-t) cos(-t) tant =

A: Solution ) sin t = 1/4    t = sin-1(1/4)    t = 14.48 Cos (14.48) = 0.968 Sin(-t) = - sin t Sin (-t)…

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Q: 7a6(cos +i Si ) IF USE DE MOIURES TheoREM To Find Z. 23

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Q: 2 4. Find the length of arc of the curve x3 + y = 1 in the first quadrant from the point where x =…

A: Let's find arc length of given curve in first quadrant.

Q: Prove that L" (coshat sinat + sinhat cosat) %3D s*+4a*. 2a

A: The function F(s) is Factorize the denominator

Q: 1. Use Green's Theorem to evaluate [(3ye* -7 sin (3x*))dx + (5x* +2x*y* +8e*-y* )dy, where C is the…

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Q: 5. Find the length of one arch of the cycloid x = sin and y = 1- cos 0

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Q: Find the points on the givern curve where the tangent pairs.) 7= 6 cos(0) horizontal tangent (r, 8)…

A: Consider the given Curve, r=6cosθ Find the points on the given curve where the tangent line is…

Q: 2. Prove that, V{(sec 0 - 1)/(sec 0 + 1)} cot 0. = cosec e

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Q: Suppose f(x, y) = x2 + y? where x = r cos 0 and y = r sin 0. Find and whenr = 1, 6 -: = 1, 0 =

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Q: 7. Find the length of the curve: r = 1 + cos 0

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Q: Q1: show that1) d/dz [cosz] = -sin z , 2) 1+tan2 z = sec2 z

A: (1) Use the first principle to derive the derivative of cos(z),…

Q: Find the area of the intersection of the circles r = 3 sin(0) andr = 3 cos(0).

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Q: Sketch the cardioid r = 3 cos 0 and find the coordinates of the points on the cardioid where the…

A: Given polar equation is r=3cosθ

Q: 23. Find (to two decimal places) the coordinates of the point P in Figure 9 where the tangent line…

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Q: TQand TR are secants from Point T to Cirlce A as shown below: s. If mQR = 70° and mSP 34°, what is…

A: Given: To explain the correct of the given statement as follows,