Task Sets: Extend trigonometric functions using unit circle - Common Core Math - HS Functions

Fluency Practice

Evaluate each expression using the unit circle. Give exact values.

$Unit circle showing point P at (sqrt(3)/2, 1/2) in the first quadrant, with x-coordinate labeled cos(theta) and y-coordinate labeled sin(theta).$

The terminal side of angle $\theta$ in standard position intersects the unit circle at the point $\left(\frac{\sqrt{3}}{2},\, \frac{1}{2}\right)$ . What is $\sin(\theta)$ ?

The angle $\frac{2\pi}{3}$ has its terminal side in Quadrant II. What are the signs of $\sin\!\left(\frac{2\pi}{3}\right)$ and $\cos\!\left(\frac{2\pi}{3}\right)$ ?

Both positive

$\sin > 0$ , $\cos < 0$

Both negative

$\sin < 0$ , $\cos > 0$

Use the reference angle strategy to evaluate $\sin\!\left(\frac{5\pi}{6}\right)$ . Give an exact answer.

Use the reference angle strategy to evaluate $\cos\!\left(\frac{7\pi}{6}\right)$ . Give an exact answer.

Evaluate $\cos\!\left(-\frac{\pi}{3}\right)$ . Give an exact answer.

Exercises: Extend Trigonometric Functions Using the Unit Circle

Warm-Up: Review What You Know

Fluency Practice