Trigonometry Basics (Standard)

Multi-step exam-style items.

Phase 2 · ACT Math

Trigonometry Basics: core idea

Special angles on unit circle.

Find $\sin 45^\circ$ .

Hint: Use a 45-45-90 triangle. Answer: √2/2.

1. If $\tan\theta=\frac34$ and $\theta$ is acute, find $\cos\theta$ .
2. Convert $\frac{5\pi}{6}$ radians to degrees.
3. In triangle $ABC$ , $A=35^\circ$ and $B=65^\circ$ . Find $C$ .
4. A ramp rises $3$ ft over a horizontal run of $12$ ft. Find $\tan\theta$ .
5. Find $\cos 120^\circ$ .
6. A sinusoid has maximum $7$ and minimum $-1$ . Find its amplitude.
7. If $\sin\theta=\frac{12}{13}$ and $\theta$ is acute, find $\tan\theta$ .
8. Find the exact value of $\tan 30^\circ$ .
9. A point on the unit circle has coordinates $(0,-1)$ . What angle in degrees corresponds to it?