# Homework Help: Solving Equations Using the Unit Circle

1. May 11, 2010

### kylepetten

1. The problem statement, all variables and given/known data

Find all solutions to the equation below such that -180° $$\leq$$ x $$\leq$$ 90°

2sin2x + sinx = 0

2. Relevant equations

3. The attempt at a solution

2sin2x + sinx = 0

sinx[2sinx + 1] = 0

sin x = 0 sinx= -1/2

x = {0° + 360°n
{-180° + 360°n
n$$\epsilon$$I

Last edited: May 11, 2010
2. May 11, 2010

### Staff: Mentor

x = n*pi are the solutions to sin(x) = 0. What about the solutions to sin(x) = -1/2?

3. May 11, 2010

### kylepetten

im not using equations, i am getting my exact values from the unit circle

4. May 11, 2010

### The Chaz

Yeah, Mark44! :rofl:

5. May 11, 2010

### Staff: Mentor

You are using equations, namely 2sin2x + sinx = 0, which you rewrote as sinx(2sinx + 1) = 0.

You have found the solutions to the equation sinx = 0, but you haven't found any for the equation 2sinx + 1 = 0.

BTW, according to your problem description, you need be concerned only with values for which -180° <= x <= 90°. On this interval there are only two solutions to sinx = 0.

6. May 11, 2010

### willem2

If you post an equation here, it looks like you're using it.
sin x = 1/2 is another possibility. I'm certain that value of x is on the unit circle as well.
you didn't use the condition that -180<=x<=90. An answer such as 360n isn't acceptable here.

7. May 11, 2010

### Staff: Mentor

Probably a typo, but sin x = 1/2 is not a solution. sin x = -1/2 is a solution, though.
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