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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(t)^2

 May 18, 2021
 #1
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The   y  intercepts occur  when  x  = 0

 

So

 

0  =  1  +  2sin (t)   rearrange  as

 

2sin (t)   =  - 1

 

sin (t)  =   -1/2

 

This   occurs  when   t   =   7pi/6     

 

The  y  intercept    =   2 + 6 [cos  ( 7pi/6) ]^2  =  2+ 6 (-sqrt (3)  / 2)^2  =  2 + 6 (3/4)  = 2 + 9/2  = 6.5

 

Here's a graph : https://www.desmos.com/calculator/oumasnrvgu 

 

 

cool cool cool

 May 18, 2021

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