louF answer is CORRECT This is a written question, worth 10 points. DO NOT place

Question

louF answer is CORRECT This is a written question, worth 10 points. DO NOT place the problem code on the proctor will fill this out after exam submission. Show all steps (work) on your answ credit. Problem Code: 1833 For the parametric curves x() -3+3 cos0) y)-6-3sin). 1E 10,2n), Part a: Give an equation relating x and y that represents the curve. Part b: Find the slope of the tangent line to the curve when Part c: State the points (x. y) where the tangent line is horizontal. 4 a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. Calc 2 Spring 2017 F.. pdf

Explanation / Answer

x = 3 + 3 cos t , y= 6-3 sin t

(x-3)/3 = cos t , (y-6)/3 = -sin t

Squaring and adding

(x-3)2 / 9 + (y-6)2/ 9 = 1

(x-3)2+(y-6)2=9

b. dx/dt = -3 sin t

   dy/dt = -3 cos t

    dy/dx = (dy/dt)/(dx/dt) = cot t

When t = pi/4

    dy/dx = cot pi/4 =1

c .Horizontal tangent means dy/dx =0

    cot t=0

    t= pi/2 , 3pi/2

   When t =pi/2 , x =3+3(0) =3, y= 6-3(1) =3

When t =3pi/2 , x =3 , y = 6+3 =9

Points are(3,3) ,(3,9)

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