Trigonometry double angle:

Question

Given that x = 3sinθ and y = 3-4cos2θ, eliminate θ and express y in terms of x. 

Answer 1

 

 The values  x = 3 sinθ   = > sin θ  = x/3

                  y = 3 - 4cos2θ =>3 - y = 4 cos2θ  =>cos2θ  =( 3 - y) / 4

( 3 - y) / 4 = 1 - 2( x / 3)²

( 3 - y) / 4 = 1 - 2( x² / 9 )

9 ( 3 - y) = 4 (9 - 2 x² )

27 - 9 y = 36 - 8 x²

27 - 36 = - 8 x² + 9y

-9 + 8 x² =  9 y

y = (8 x² - 9) / 9

y = 8( x / 3 )²  - 1 .

So, y is expressed in terms of x as y = 8( x / 3 )²  - 1 .