11.8 Unit Circle

Radian Measure and the Unit Circle (Extended)

1. 1. Convert between degrees and radians; understand radian measure as arc length on the unit circle.
2. 2. Use the full unit circle to define $\sin\theta$, $\cos\theta$ and $\tan\theta$ for any angle.
3. 3. Use special triangles to find exact trigonometric values at multiples of $\frac{\pi}{6}$, $\frac{\pi}{4}$, $\frac{\pi}{3}$.
4. 4. Apply negative-angle and complementary-angle identities.
5. 5. Apply the Pythagorean identity $\sin^2\theta + \cos^2\theta = 1$ and $\tan\theta = \dfrac{\sin\theta}{\cos\theta}$.
6. 6. Solve trigonometric equations of the form $\sin x = k$, $\cos x = k$, $\tan x = k$ in radians.
7. 7. Calculate arc length, sector area and segment area in radians.
8. 8. Calculate arc length, sector area and segment area in degrees.