MATH HELP!!! i am not sure how to do this!?

Question

- 1 - 5 sin(theta)= 2 cos squared(theta) , (theta) E [-180 degrees, 720 degrees]

any help appreciated!!!!

solving the equations.

Answer 1

-1 - 5sin x = 2(1 - sin^2 x)

-1 - 5 sin x = 2 - 2 sin^2 x

2 sin^2 x - 5 sin x - 3 = 0

(2 sin x + 1)(sin x - 3) = 0
sin x = -1/2 sin x = 3

sin x = -30 degrees, etc.

Answer 2

- 1 - 5 sin(theta)= 2 cos squared(theta) , (theta) E [-180 degrees, 720 degrees]
Let x = theta
-1 -5sin x = 2 cos^2 x {-180 =< x =< 720}
cos^2x = 1 - sin^2 x
So -1-5sin x = 2(1-sin^2 x) = 2-2sin^2 x
2sin^2 x -5sin x-3 = 0
(2sinx +1)(sin x -3) = 0
sin x = -1/2 --> x = -30,-150 , 210, 330, 570, 690
sin x = 3 is impossible so it is rejected.

Answer 3

You could write cos^2 x in terms of sin x

-1 - 5sinx = 2(1-sinx^2)
or 2sinx^2 - 5 sinx - 3 = 0

solving for sinx, sinx = (5 +/- 7)/4 = 3, -0.5.
Since sinx can't equal 3, sinx = -0.5.

The solutions would be -150, -30, 210, 330, 570, 690

Answer 4

are you trying to solve for theta or make the left side equal to the right side (verify)

Answer 5

the answer is 900 degrees