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