Show that cos 3θ = cos3 θ − 3 cos θ sin2 θ and use this identity to find an equation in rectangular coordinates for the curve r = cos 3θ.

Q: Eliminate the parameter to find a Cartesian equation of the curve. x=1-cos(t) y=1-sin(t)

A: We have to eliminate the parameter and find the cartesian equation.

Q: ) Write the equation r2+r(sin 0-6 cos 0) = 0 in Cartesian coordinates and identify the corresponding…

A: Solution is given below:

Q: The parametric equations: x = a a cos 0,y = a sin 0;0 ses 2n, define a curve called an asteroid

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Q: Find the lengthof the curve r = a sin² (0/2), 0 0

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Q: Show that the curves r = a sin 0 and r = a cos 0 intersect at right angles.

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Q: Find the length of the curve r = cos(f) + sin(0), 0sOs

A: The objective is to find the length of the curve.

Q: Consider the following parametric equation.  x = 18(cosθ + θsinθ) y = 18(sinθ - θcosθ) What is…

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

A: Given x and y values.... Let us find dy/dx to draw the graph....

Q: Suppose a curve is traced by the parametric equations x= 6.08 sin(t) and y = 22 -…

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Q: Show that cos 120 cos 40 – 3 cos 40 sin? 40 and use this identity to find an equation in rectangular…

A: We have to show that cos12θ=cos34θ−3cos4θsin24θ Consider  cos12θ=cos34θ=cos3P        Let P=4θ We…

Q: Trace the curve r= 1/2 sin(theta) cos^3 (theta)

A: Given curve is: r=12sinθcos3θ ⇒r=142sinθcosθcos2θ=14sin2θ1+cos2θ2=18sin2θ+18sin2θcos2θ Here replace:…

Q: Sketch the curve and Find the length if the curve: x=cos(2t), y=sin(2t), 0<_t<_ pi/2

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Q: Eliminate the parameter to find a Cartesian equation of the curve, and sketch the curve and indicate…

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Q: Find a Cartesian equation of the curves. 1) r= 2 sin 0 2) r = 5 csc e

A: 1) r=2sinθ2) r=5cosecθwe have to convert these curves into cartesian equations

Q: Find the exact length of the curve r = sin 0 + cos 0.

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Q: Show that the curves r = a sin θ and r =  a cos θ intersectat right angles.

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Q: Find the equation of the tangent line to the parametric curve x = θ+cosθ, y=1+sinθ; θ = π/6

A: We have to find equation of tangent line to the parametric curve at θ=π6 where parametric curve is:…

Q: Find an equation of the tangent line for.10 a curve defined by the following parametric equations

A: Given, x=t3-4t2+4t+3 , y=t+3

Q: Find the exact length of the curve. x = 7 cos(t) – cos(7t), y = 7 sin(t) – sin(7t),

A: given : formula for arc length is as below :

Q: Eliminate the parameter in the parametric equations x = 7+ sint, y = 2+ sint, for 0sts, and describe…

A:

Q: Find the equation of the tangent line(s) to the following set of parametric equations at the given…

A: We have to find the equation of tangent from the parametric curve

Q: Graph the pair of parametric equations with the aid of a graphing calculator x = 4 sin t - sin 4t, y…

A: Given x=4sint-sin4ty=4cost-cos4t0≤t≤2π

Q: A helicopter is to fly directly from a helipad at the origin in the directionof the point (1, 1, 1)…

A: Given that: A helicopter is to fly directly from a helipad at the origin in the direction of the…

Q: Consider the curves:r = 4sin 0 and r = 2 sin(0) + 2cos (0).

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Q: Consider the following parametric equation. #20(cos 0+0 sin 0) y- 20(sin 0-0 cos 0) What is the…

A: Given: x=20cosθ+θsinθy=20sinθ-θcosθ we know length of curveL on interval a,b is given by…

Q: The equation for the tanget to graph of y=sin^1(x/2) at the origin is

A: Given, y=sin1x2 Differentiate the given function with respect to x we get, dydx=cosx212 At point…

Q: Write an equation for the line tangent to the graph created by the parametric 3 cos 0 and y(0) = 3…

A: To find the equation of tangent line.

Q: The curves with equations x  =a sin nt , y = b cos t are called Lissajous figures. Investigate how…

A: Given, Lissajous figures x = a sin(nt) and y = b cos(t) We have to investigate how the curve varies…

Q: Find all points of intersection of the curves r = cos 2 θ and r =1/2

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Q: . The curve with parametric equations x = (1 + 2 sin 0) cos 0, y = (1 + 2 sin 0) sin 0 is called a…

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Q: The derivative Z of the parametric equations z= 7 sin 3t and y= cos 3t is.

A:

Q: Consider the following parametric equation.  x = 14(cosθ + θsinθ) y = 14(sinθ - θcosθ) What is…

A: Given parametric equations are x=14cosθ+θsinθy=14sinθ-θcosθ

Q: Which of the following is the equation of tangent line of the curve that is given by parametric…

A: Given the parametric equations x=3cost+2sint and y=e6t . We need to find the equation of the tangent…

Q: Find the length of the curve r = 4 – 4 sin 0

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Q: Find the exact length of the curve. x = 9 cos(t) - cos(9t), y = 9 sin(t) - sin(9r), Ostsn 9 cos (47)…

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Q: Select the curve generated by the parametric equations. Indicate with an arrow the direction in…

A: make a table values t x=t+sint y=cost -π x=-π +sin-π=-π +0=-π =-3.14 y=cos-π=-1 -π2…

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

A: Solve by finding slope

Q: Can the parametric curve (t, sin t) be represented as a graph y = f (x)? What about (sin t, t)?

A: Parametric curve is (t, sint) i.e x = t and y = sint

Q: Eliminate the parameter to find a cartesian equation of the curve. x = sin(1/2θ),  y = cos(1/2θ),…

A: x=sin12θ,  y=cos12θ

Q: Find the left most point on the upper half of the cardioid r=1+cos(theta)

A: we need to find leftmost point on the upper half of the cardioid r = 1 + cos(theta) by plotting in…

Q: Find all points of intersection of the curves r = sin 0, r= sin 20

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Q: The length of the curve determined by equations x = 8 cos t + 8t sin t and y = 8 sin t – 8t cos t…

A: Given: x=8cost+8tsinty=8sint-8tcost0≤t≤π2

Q: Plot the cissoidr 2 sin 0 tan 0 and show that its equation in rectangular coordinates is x3 y2 2 - x

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Q: Find the length of the curve r = sqrt(1+sin(2 theta) for 0

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Q: Find the Cartesian equation of the curve: x = 2cos(theta) y = 1 + sin(theta) where theta is…

A: Given that the equation of the curve, x=2cosθy=1+sinθWhere,  0≤θ&lt;π2

Q: The curves r1(t) (- 5t, t°, t*) and 72(t) (sin(5t), sin(2t), t) intersect at the origin Find the…

A: Find the thetha

Q: The parametric equations of a curve are given by 2 x = In and y = cosh-(2t). when t = 1. dx Find

A: Given,            The parametric equations of a curve are given by              x=ln2t  and…

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.