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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.

# Trigonometric Equations - Double Angle Formula

In the domain $$[0^\circ , 1000^\circ ]$$, how many solutions are there to $$\sin \theta \cos \theta = \frac {1} {2}$$?

In the interval $$[0, 2 \pi ]$$, how many solutions are there to

$\sin \theta = 2 \sin 2 \theta ?$

How many $$x$$'s in the interval $$0 \leq x \leq 29\pi$$ satisfy $\sin \left(2x-\frac{\pi}{5}\right)=\sin \frac{\pi}{8}?$

How many $$x$$'s in the interval $$0 \leq x \leq 60\pi$$ satisfy $6\cos 2x+23\sin x-4=0?$

In the interval $$[0, 2 \pi ]$$, how many solutions are there to

$\cos^2 \theta = \cos 2 \theta ?$

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