Find one value of θ or x that satisfies each of the following.
sin θ = cos(2θ + 30°)

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Recall the co-function identity in trigonometry: \(\sin \theta = \cos(90^\circ - \theta)\). This means we can rewrite the equation \(\sin \theta = \cos(2\theta + 30^\circ)\) as \(\sin \theta = \cos(90^\circ - \theta)\) to find a relationship between \(\theta\) and \(2\theta + 30^\circ\).

Set the angles inside the cosine equal to each other using the identity: \(2\theta + 30^\circ = 90^\circ - \theta\). This gives an equation involving \(\theta\) that you can solve.

Solve the linear equation \(2\theta + 30^\circ = 90^\circ - \theta\) by first adding \(\theta\) to both sides and subtracting \(30^\circ\) from both sides to isolate \(\theta\) terms on one side.

Simplify the resulting equation to find the value of \(\theta\). This will give you one possible solution for \(\theta\) that satisfies the original equation.

Remember that sine and cosine are periodic functions, so there may be multiple solutions. After finding one solution, consider the general solutions by adding the appropriate multiples of \(360^\circ\) or \(2\pi\) radians if needed.

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