# Homework Help: Need help solving this trig equation

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1. Mar 26, 2017

### flgdx

1. The problem statement, all variables and given/known data
what's the best way to solve this equation: 3cos(θ) + 1.595*sin(θ) = 3.114

2. Relevant equations
(sinθ)^2 + (cosθ)^2 = 1

3. The attempt at a solution
I tried using the identity above to solve this equation and ended up with cosθ = +/- 1.0526.

2. Mar 26, 2017

### Comeback City

3. Mar 26, 2017

### flgdx

so since (sinθ)^2 + (cosθ)^2 = 1, I solved for sinθ and got sqrt(1 - (cosθ)^2). Then I subtituted it in to the equation 3cos(θ) + 1.595*sin(θ) = 3.114 and solved for θ.

4. Mar 26, 2017

### vela

Staff Emeritus
Well, that's obviously wrong because -1 ≤ cos θ ≤ 1, and 1.0526 is outside that range. Your approach should work though.

Another approach is to use
$$a \cos\theta + b \sin\theta = \sqrt{a^2+b^2} \cos(\theta-\phi)$$ where $\tan\phi = b/a$.

5. Mar 26, 2017

### flgdx

could you pls show me how you got that equation?

6. Mar 26, 2017

### vela

Staff Emeritus
Consider a right triangle below and use the identity $\cos(\theta-\phi) = \cos\theta\,\cos\phi + \sin\theta\,\sin\phi$.