Find the general solutions of the following trigonometry equations: a) cos(3θ/2 + π/3) = 1/2

Here are the solutions to your trigonometry problems.

1. Find the general solutions of the following equations:

• a) $\cos \left(\frac{3\theta}{2} + \frac{\pi}{3}\right) = \frac{1}{2}$

  Step 1: Find the principal value.

  $$\cos \left(\frac{\pi}{3}\right) = \frac{1}{2}$$

  Step 2: Apply the general solution for $\cos A = \cos \alpha$, which is $A = 2n\pi \pm \alpha$.

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