solving Trig Equation which techniquse to use?

[Starblazer]

I need to solve for theta, the following equation.

262.5 cos (theta) - 750 sin (theta) + 250 cos (theta) - 1000 sin (theta) = 0

How do I start, which identities do I need (if any)

 

[tkhunny]

262.5 cos (theta) - 750 sin (theta) + 250 cos (theta) - 1000 sin (theta) = 0

Addition

$\displaystyle 512.5\cos(\theta) - 1750\sin(\theta) = 0$

Transformation

$\displaystyle \sqrt{512.5^{2} + 1750^2}\cos\left(atan\left(-\dfrac{1750}{512.5}\right)-x\right) = 0$

That's lots easier.

 

[Starblazer]

Addition just too obvious. Thanks

\(\displaystyle \begin{array}{l}
262.5\cos \theta - 750\sin \theta + 250\cos \theta - 1000\sin \theta = 0\\
512.5\cos \theta - 1750\sin \theta = 0\\
512.5\cos \theta = 1750\sin \theta \\
\frac{{512.5}}{{1750}} = \frac{{\sin \theta }}{{\cos \theta }}\\
\frac{{512.5}}{{1750}} = \tan \theta \\
{\tan ^{ - 1}}(\frac{{512.5}}{{1750}}) \approx {16.32^ \circ }
\end{array}\)

 

[tkhunny]

If you're supposed to find all solutions, say in $\displaystyle [0,2\pi]$, then you missed one.

 

[Starblazer]

Normally you are supposed to find the solutions from $\displaystyle 0 - 2\pi$ thanks for pointing that out
but this was for a mechanics static friction problem.