Year11 MATH 3-2-5

Trigonometric Functions

Unit 2

Focus: Radians, unit circle, and graphs.

1. Convert $120^\circ$ to radians (in terms of $\pi$).
2. Convert $\frac{3\pi}{4}$ radians to degrees.
3. State the exact value of $\sin(\frac{\pi}{6})$.
4. State the exact value of $\cos(\pi)$.
5. Find the period of the function $y = \sin(2x)$.
6. Find the amplitude of $y = -3\cos(x) + 1$.
7. Solve $\sin(x) = 0.5$ for $0 \le x \le 2\pi$.
8. Use the Pythagorean identity $\sin^2\theta + \cos^2\theta = 1$ to find $\cos\theta$ if $\sin\theta = \frac{3}{5}$ and $\theta$ is in the first quadrant.
9. Find the vertical shift of $y = \tan(x) – 4$.
10. What is the value of $\tan(\frac{\pi}{4})$?

Answers:

1. $\frac{2\pi}{3}$ | 2. $135^\circ$ | 3. $0.5$ | 4. $-1$ | 5. $\pi$ | 6. 3 | 7. $x = \frac{\pi}{6}, \frac{5\pi}{6}$ | 8. $\frac{4}{5}$ | 9. Down 4 units | 10. 1.