What are the y-intercepts of the graph of the parametric equations \(x = 1 − 2 sin t, y = 2 + 6 cos^2 2t? \)
+128408 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
