1. Find: (i) the reference number of t; (i) the terminal point P(z, y) on the unit circle determined by t; (iii) sint and cos t. (a) t= (b) t= C1)

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: Eliminate the parameter t and graph noting the direction of the curve. x= 2 cos (t) ly=1-2 sin(t) 37…

A: see next step

Q: 4. Find the moving trihedral of the curve f(t) at the indicated value: †(t) = cos? t î + sin² t ĵ…

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Q: Consider the following. tan2(0), y = sec(0), -n/2 < 0 < t/2 X = (a) Eliminate the parameter to find…

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Q: Suppose an object moves in an elliptical orbit parametrized byx = 4 cos t and y = 7 sin t, where t ≥…

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Q: Which one of the following could be the graph of the curve given parametrically by x(t) sin(t + sin…

A: Given that x(t)=sin(t+sint) and y(t)=cos(t+cost).

Q: = V4 cos" : – 1, y = 10 < x < 30

A:

Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

A: Given: x=2sint  y=3cost 0≤t≤2π Consider x=2sint. sint=x2cost=y3

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.

Q: 2. Find the point on the curve r(t) = (12 sin t, -12 cos t, 5t) at a distance 137 units along the…

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Q: 13. Eliminate the parameter t, sketch the curve, and indicate the orientation. x=5 sint, y= 5cost,

A: We will square the both equations and then we will add them to eliminate the t

Q: Find the circumference of the curves x=e^-2θ (sinθ+cosθ), y=e^-2θ (sinθ-cosθ) over the interval 0 ≤…

A: To find: The circumference of the given curves. Given information: Concept used: If a functions are…

Q: Find an interval of t-values such that c(t) = (cos t, sin t) traces the upper half of the unit…

A: Interval.

Q: Find the length of the given curve: where -4 < t ≤1. r(t) = (-2t, 2 sin t, 2 cos t)

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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: Find T', N and B for the curve r(t) = (2 cos(5t), 2 sin(5t), 4t) at the point t = 0

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Q: 16. Find, correct to two decimal places, the coordinates of the point on the curve y = tan x that is…

A: Given: Curve y=tanx       for any x , then y= tanxThen point (x,y) : (x,tanx) always lies on curve…

Q: 8. Given the space curve r(t) = (sin²t, cos't, tant), find an equation of the tangent line in…

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Q: Find the lengths of the curves x = cos t, y = t + sin t, 0 … t … pi

A: Solution:Given   x= cos t,      y= t+sin t,   0≤t≤πFormula:Lenght=∫dxdx2+dydt2dt1+cos 2x=2 cos2…

Q: = = 2 cos (t) lu =1 sin(t) T Find the slope of the tangent line to the parametric curve at the point…

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Q: ²y. Show that (0, 7/2) is on the Consider the equation 2 sinx+ cos y = (b) graph of the equation,…

A: Consider the given equation:

Q: Find the exact length of the curve. 43. x = t sin t , y = t cos t , 0 ≤ t ≤ 1

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Q: r = 2 cos 0,0 <o <n. 2 L = S°. dr r2 + de de.

A: Use the formula given to find length of curve.

Q: Find the length of the curve 7(t) = (cos(4t), sin(4t), 5t) for – 8 <t< 1 Give your answer to two…

A: use the arc length formula for finding length.

Q: 10. Given the curve: y = 4cos°x – 3cosx, find the following values of x (from 0 to 2pi radians) when…

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Q: A) Find the distance traveled by a particle with position (x, y) as t varies in the given time…

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Q: 2 cos(t) T at the point 4 Find the slope of the tangent line to the parametric curve ly = 1 sin(t)

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Find the equation of the tangent line to the curve 2 sin z + 5 cos z at the point (0, 1/5). The…

A: Solution:- use u/v formula to differeniate

Q: Graph the curve: x = 3et cos(t),    y = 3et sin(t),    0 ≤ t ≤ π and then find the exact length of…

A: The provided parametric equation of the curve is as below

Q: Calculate the length of the curve r=a*sin(^3)(x/3) for (x(1)=0, x(2)=3pi)

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Q: Find the length of the curve 7(t) = (ei cos(), ei sin(÷), e) n(4),e¿): for 0 <t < 5. CoS

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

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Q: r = -3 cos(20) – cos(0) os(e)

A: To check the symmetry of the curve  r=-3 cos 2θ-cos(θ)...(1) with respect to a straight line θ=0 or…

Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

A: The given parametric equation is x=cos 2t,   y=sin t,    -π≤t≤π. This implies that, x=cos…

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: Find the exact length of the curve. y = In(cos(x)), TC 0 < x<.

A:

Q: 10. Find the point on the curve r(t) = (12 sin t)i – (12 cos t)j + 5tk at a distance 13 T units…

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Q: Consider the parametric curve x = sint + cos t, = cos² t 0 <t < 2n п Find an equation for the…

A: We find dx/dt and dy/dt from the given equations

Q: Find the exact length of the curve. x = 9 cos(t) − cos(9t), y = 9 sin(t) − sin(9t), 0 ≤ t ≤ pi

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Q: {; 4 cos(t) 2 sin(t) at the point 4 Find the slope of the tangent line to the parametric curve

A: We have the parametric equation of curve as x=4cost⇒cost=x4        ⋯⋯1y=2sint⇒sint=y2          ⋯⋯2…

Q: Find an interval of t-values with t > 0 such that c(t) = (cos t, sin t) traces the upper half of the…

A: Given,  ct = cost, sint  and t ≥ 0 We have to find the interval of t-values such that ct = cost,…

Q: 10 cos 0 and y = 10 sin³ 0, find the total length of the curve swept out by the point If x = (x, y)…

A: We have to point length of curve swept out by the point:

Q: 1 cos(t) ly = 3 sin(t) Find the slope of the tangent line to the parametric curve at the point

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Q: 3. Find if (a) y = 22" In (cot (7x)*) (b) y = sin? (Arcsin (T) +e-*)

A: Part(a) We have y=22xlncotπx2 We will use product rule and chain rule.  Product rule says:…

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: 7. [10pts] Calculate the slope of the tangent line to the polar curve r = when 0 cos (0/3) at the…

A: given curve is                                  r=cosθ3 at   θ=π…

Q: e of the tangent line to the polar sin(40) at 6 curve r =

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Q: 1. Plot in your graphing calculator. x = 2 sin t and y = cos t in[0,1| a. Reproduce the graph on…

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Q: Find the exact length of the curve. y = In(cos(x)), 0 s xs- TO 6. Need Help? Read It

A: Given problem:- Find the exact length of the curve.   y = In(cos(x)),   [0, π/6]

Q: Find the equation of the tangent line to the curve 1 2 sin x + 5 cos x at the point (0, 1/5). The…

A: