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## Trigonometric Equations

Equations with trigonometry in them can look scary, but that's nothing that a quick little substitution can't fix.

# Level 3

Find the sum, in degrees, of all $$\theta$$ between $$0^{\circ}$$ and $$360^{\circ}$$ such that

$\tan(2\theta-330^{\circ})=\sqrt{3}.$

If $$\cos A = \tan B,$$ $$\cos B = \tan C,$$ and $$\cos C = \tan A,$$ what is $$\sin A?$$

The smallest positive solution of the equation $2 \sin^2 3x - \cos 8x - 1 = 0$ in the interval $$\left( 0, \frac{\pi}{2}\right)$$ can be expressed in the form $$\frac{a\pi}{b}$$, where $$a$$ and $$b$$ are coprime positive integers, find $$a+b$$.

The sum of all positive solutions of $2\cos 2x \left( \cos 2x- \cos\frac { 2014 \pi ^ 2 }{ x } \right) =\cos { 4x } -1$ is $$k\pi$$. Find $$k$$.

$\large \cos(p \cdot \sin x)=\sin(p \cdot \cos x)$ Find the smallest positive integer $$p$$ for which the above equation has a solution for $$x \in [0, 2\pi]$$.

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