Questions: Find all degree solutions for the following. (Enter your answers as a comma-separated list. Let k be any integer.) theta: cos 3 theta=0 theta

Solution Steps

The equation \(\cos 3\theta = 0\) implies that \(3\theta\) must be an odd multiple of \(\frac{\pi}{2}\), since \(\cos x = 0\) when \(x = \frac{\pi}{2} + k\pi\), where \(k\) is any integer.

Thus, we can write: \[ 3\theta = \frac{\pi}{2} + k\pi \] where \(k\) is any integer.

Divide both sides of the equation by 3 to solve for \(\theta\): \[ \theta = \frac{\pi}{6} + \frac{k\pi}{3} \]

Since the question asks for degree solutions, convert \(\theta\) from radians to degrees: \[ \theta = 30^\circ + 60^\circ k \] where \(k\) is any integer.

Final Answer