2. Trigonometric Functions on Right Triangles

Determine whether each statement is true or false. If false, tell why. Use a calculator for Exercises 39 and 42. sin 42° + sin 42° = sin 84°

CONCEPT PREVIEW The terminal side of an angle θ in standard position passes through the point (― 3,― I3) Use the figure to find the following values. Rationalize denominators when applicable. r

In Exercises 1–8, a point on the terminal side of angle θ is given. Find the exact value of each of the six trigonometric functions of θ. (3, 7)

Given that lines $b$ and $c$ are parallel and angle $6$ is formed by a transversal intersecting these lines, what is the measure of angle $6$?

Find the indicated function value. If it is undefined, say so. See Example 4. cos 1800°

Give all six trigonometric function values for each angle θ . Rationalize denominators when applicable.

cos θ = ―5/8 , and θ is in quadrant III

Suppose $LK$ is tangent to circle $J$ at point $K$. If the distance from the center $J$ to point $L$ is $10$ units and the distance from $L$ to $K$ is $6$ units, what is the length of the radius of the circle?

In right triangle $PSQ$, angle $PSR$ measures $99°$. What is the measure of angle $PSQ$ in degrees?

Determine whether each statement is possible or impossible. See Example 4. tan θ = 0.93

Find the values of the six trigonometric functions for an angle in standard position having each given point on its terminal side. Rationalize denominators when applicable. (6√3 , ―6)

Given a right triangle, what is the value of $tan(60°)$?

Given the right triangle below, evaluate $\(\cos\]\theta\)$.

In a regular polygon with $4$ sides, what is the measure of each interior angle?

In Exercises 33–42, let sin t = a, cos t = b, and tan t = c. Write each expression in terms of a, b, and c. tan(-t) - tan t

Solve each problem. See Examples 3 and 4. Distance through a Tunnel A tunnel is to be built from point A to point B. Both A and B are visible from C. If AC is 1.4923 mi and BC is 1.0837 mi, and if C is 90°, find the measures of angles A and B.