QuestionSolve the equation on the interval $[0,2 \pi)$. Give the exact solution in radians and give an approximation in degrees rounded to 1 decimal place. $$\cos x=\frac{1}{6}$$
Part: 0 / 2
Part 1 of 2
The exact solution set in radians is $\square$ \}.
Write your answer in simplest form.

Studdy Solution
To convert the solutions to degrees and provide an approximation, use the conversion factor $180^\circ/\pi$.
1. Approximate $\cos^{-1}\left(\frac{1}{6}\right)$ in degrees:
$$\cos^{-1}\left(\frac{1}{6}\right) \approx 80.4^\circ$$
2. Approximate $2\pi - \cos^{-1}\left(\frac{1}{6}\right)$ in degrees:
$$2\pi - \cos^{-1}\left(\frac{1}{6}\right) \approx 360^\circ - 80.4^\circ = 279.6^\circ$$
The exact solution set in radians is:
$$\left\{ \cos^{-1}\left(\frac{1}{6}\right), 2\pi - \cos^{-1}\left(\frac{1}{6}\right) \right\}$$
The approximate solution set in degrees is:
$$\left\{ 80.4^\circ, 279.6^\circ \right\}$$