# Simultaneous Trig Equations

1. Sep 23, 2010

### Joe_I_Am

How would one go about solving the following equation?

242= 290cos(theta) + 187cos(phi)
0 = 290sin(theta) - 187sin(phi)

I have tried squaring both sides of both equations and adding them, and then using cos2x + sin2x = 1 to narrow some stuff down, and basically only found that:

phi + theta = 123.9 degrees.

But I still feel like I'm stuck. Maybe I'm missing an identity or something, I am terrible with those. Any help would be appreciated.

2. Sep 23, 2010

### Joe_I_Am

Just realized I put this in the wrong forum,....sorry guys.

3. Sep 24, 2010

### Studiot

Since this is homework, here are some strategy hints

From 1 get cos$$\phi$$ in terms of cos$$\theta$$

From 2 get sin$$\phi$$ in terms of sin$$\theta$$

substitute into either the formula for

cos ($$\theta$$ + $$\phi$$)

or

sin ($$\theta$$ + $$\phi$$)

Substituting into 3 will get you an equation in a single unknown.