problem with angles?

Question

I know the answer to this problem because it's from an old New York State Math B Regents, but I don't know how to get it.

The Question:
On a monitor, the graphs of two impulses are recorded on the same screen, where 0 degrees (is less than or equal to) x degrees < 360 degrees. The impulses are given by the following equations:

y = 2 sin^2 x
y = 1 - sin x

Find all values of x, in degrees, for which the two impulses meet in the interval 0 degrees (is less than or equal to) x degrees < 360 degrees. [Only an algebraic solution will be accepted.]


And the answers are 30, 150, and 220 degrees. I would really appreciate any help or explanations!

haha sorry! thank you for pointing out that 220 is incorrect everyone. i wrote the real answers down quickly, so my 7 looked like a 2.

Answer 1

Set the two y-values equal to each other to get
2sin^2(x) = 1 - sin(x)

This is
2sin^2(x) + sin(x) - 1 = 0
(2sin(x) - 1))(sin(x) + 1) = 0
So either sin(x) = 1/2 or sin(x) = -1.

In the range of 0 <= x < 360, the answers that fit are x = 30 and x = 150 for sin(x)=1/2, and x=270 for sin(x)= -1. I don't know where you're getting 220 from.

Answer 2

y = 2 sin^2 x
y = 1 - sin x
Therefore 2sin^2x = 1 -sinx , or
2sin^2x +sinx -1 = 0
(2sinx -1)(sinx+1)=0
sin x +1=0, so sinx = -1 --> x = 270 degrees
2sinx-1= 0 , so x = 1/2 --> x = 30 , 150 degrees
So the answer is x = 30, 150, 270.
Your answer of 30,150,220 is incorrect.

Answer 3

Set them equal
1 - sinx = 2 sin^2 x
2sin^2 x + sinx - 1 = 0
(2sinx - 1)*(sinx + 1) = 0

sinx = -1, 1/2
x = 30, 150, 270

220 is not right