Given the equation

where $\theta$ is in radians,

1. Use your calculator to find the smallest positive solution to the equation.

2. Explain why the small angle approximation is appropriate for this problem, and use the small angle approximation for cosine to approximate the smallest positive solution.

3. Find the percentage error between the two solutions found above.

For (a), just use ${\cos }^{-1}$ as normal.

For (b), it is a good idea to sketch $y=\cos (2\theta )$ and justify that $y=0.95$ is given by a small value of $\theta$.

To find the approximate solution, you can solve

For (c), you need