Find one value of θ or x that satisfies each of the following.
cos x = sin (π/12)

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Recall the co-function identity in trigonometry: \(\cos x = \sin \left( \frac{\pi}{2} - x \right)\).

Use the identity to rewrite the equation \(\cos x = \sin \left( \frac{\pi}{12} \right)\) as \(\cos x = \cos \left( \frac{\pi}{2} - \frac{\pi}{12} \right)\).

Simplify the angle inside the cosine on the right side: \(\frac{\pi}{2} - \frac{\pi}{12} = \frac{6\pi}{12} - \frac{\pi}{12} = \frac{5\pi}{12}\), so the equation becomes \(\cos x = \cos \left( \frac{5\pi}{12} \right)\).

Recall that if \(\cos A = \cos B\), then \(A = B + 2k\pi\) or \(A = -B + 2k\pi\) for any integer \(k\).

Set up the two equations: \(x = \frac{5\pi}{12} + 2k\pi\) and \(x = -\frac{5\pi}{12} + 2k\pi\), then choose an integer \(k\) (usually \(k=0\)) to find one specific value of \(x\).

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