1. Find the exact value of $\sin 45^\circ$. 2. Solve for $x$ if $\cos x = \frac{1}{2}$ and $0^\circ \leq x < 360^\circ$. 3. Prove the identity $\tan^2 \theta + 1 = \sec^2 \theta$. 4. Find all solutions of $2\sin x - 1 = 0$ for $0 \leq x < 2\pi$. 5. If $\sin \alpha = \frac{3}{5}$ and $\alpha$ is in the first quadrant, find $\cos \alpha$ and $\tan \alpha$. 6. Find the general solution to $\sin 2x = \sqrt{3}/2$. 7. Calculate the amplitude, period, phase shift, and vertical shift of $y = 3\sin(2x - \pi) + 1$. 8. Simplify $\frac{\sin 2\theta}{\cos \theta}$. 9. Verify that $\sin(180^\circ - \theta) = \sin \theta$. 10. Find the height of a tree if the angle of elevation from a point 30 meters away is $60^\circ$.