Trigonometry Basics (Advanced)

Harder items at competition-adjacent depth.

Phase 2 · ACT Math

Trigonometry Basics: core idea

Inverse trig interpretation.

Solve $2\sin x=\sqrt3$ for $0^\circ\le x<360^\circ$ .

Hint: Sine is positive in quadrants I and II. Answer: 60°,120°.

1. If $\sec\theta=\frac{13}{5}$ and $\theta$ is acute, find $\tan\theta$ .
2. Find $\sin 75^\circ$ .
3. A $20$ -m pole casts a $20\sqrt3$ -m shadow. Find the angle of elevation of the sun.
4. Solve $\cos x=0$ for $0^\circ\le x<360^\circ$ .
5. For $y=3\sin(2x)$ , what is the period in degrees?
6. If $\sin\theta=\frac35$ and $\cos\theta<0$ , find $\cos\theta$ .
7. In a triangle, $a=8$ , $b=11$ , and included angle $C=60^\circ$ . Find $c^2$ .
8. Find the amplitude of $y=-5\cos x+2$ .
9. A ferris wheel radius is $18$ m and center is $21$ m above ground. What is the maximum height?