Need help solving this trig equation

[flgdx]

Homework Statement

what's the best way to solve this equation: 3cos(θ) + 1.595*sin(θ) = 3.114

Homework Equations

(sinθ)^2 + (cosθ)^2 = 1

The Attempt at a Solution

I tried using the identity above to solve this equation and ended up with cosθ = +/- 1.0526.

 

[Comeback City]

Could you show your steps for your solution?

 

[flgdx]

Could you show your steps for your solution?

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

 

[vela]

Homework Statement

what's the best way to solve this equation: 3cos(θ) + 1.595*sin(θ) = 3.114

Homework Equations

(sinθ)^2 + (cosθ)^2 = 1

The Attempt at a Solution

I tried using the identity above to solve this equation and ended up with cosθ = +/- 1.0526.

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 $\tan\phi = b/a$.

 

[flgdx]

could you pls show me how you got that equation?

 

[vela]

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