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What are the y-intercepts of the graph of the parametric equations \(x = 1 − 2 sin t, y = 2 + 6 cos^2 2t? \)

 Dec 1, 2020
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The y intercepts occur  where  x  = 0 

 

So

 

1 - 2sin t  =  0

 

1 = 2sin t

 

sin t = 1/2    →   t = pi/6    and  5pi/6

 

So  

 

y =   2 + 6 (cos 2 (pi/6) )^2  =    2  + 6 ( cos (pi/3))^2  =  2 + 6 (1/2)^2  =  2 + 6/4  = 2 + 3/2 =  7/2

 

 Note.....  t =  5pi/6  would produce the  same y intercept

 

See the graph here :  https://www.desmos.com/calculator/qwbjod6a6f

 

 

cool cool cool 

 Dec 1, 2020

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