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

If \( 2 \cos^2{x} + 47 \cos{x} = 20 \sin^2{x} , \) then what is the value of \( \cos{x} ? \)

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In the domain \( [0, 17 ] \), how many real solutions are there to \( \cos (\pi x^2 ) = -1 \)?

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What are all possible values of \(\sin\theta + 8\cos\theta\)?

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