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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 - Problem Solving

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

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

Let $$\alpha$$, $$\beta$$ and $$\gamma$$ be the period, maximum value and minimum value, respectively, of the function $y=\sin^4 6x+\cos^4 6x.$ What is the value of $$\frac{\beta \pi}{\alpha \gamma}$$?

List the positive roots of the trigonometric equation $\cos^2 x-\sin^2 2x=0$ in ascending order to form a sequence $$\{a_n\}$$. What is the value of the constant $$m$$ that satisfies $\displaystyle \sum_{k=1}^{36}a_k=m\pi?$

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

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