2. Trigonometric Functions on Right Triangles

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. (3 , ―4)

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.

sin(-t - 2𝜋) - cos(-t - 4𝜋) - tan(-t - 𝜋)

In Exercises 23–34, find the exact value of each of the remaining trigonometric functions of θ. tan θ = 4/3, cos θ < 0

Use the appropriate reciprocal identity to find each function value. Rationalize denominators when applicable. See Example 1. csc θ , given that sin θ = ―3/7

Concept Check The two methods of expressing bearing can be interpreted using a rectangular coordinate system. Suppose that an observer for a radar station is located at the origin of a coordinate system. Find the bearing of an airplane located at each point. Express the bearing using both methods. (2, 2)

Solve each problem. See Examples 1 and 2. Distance between Two Cities The bearing from Atlanta to Macon is S 27° E, and the bearing from Macon to Augusta is N 63° E. An automobile traveling at 62 mph needs 1¼ hr to go from Atlanta to Macon and 1¾ hr to go from Macon to Augusta. Find the distance from Atlanta to Augusta.

In a right triangle, what is the longest side called?

Which of the following angle measurements might you find in a right triangle?

In a right triangle, one of the acute angles measures $80°$. What is the measure of the other acute angle?

Given a right triangle where one of the acute angles is $30°$ and the hypotenuse is $10$, what is the length of the side opposite the $30°$ angle (let this length be $x$)?

In the diagram, point O is the center of the circle. If $m\angle \mathrm{ABC}$ = $70°$, what is $m\angle \mathrm{AOC}$?

In a right triangle, if one of the acute angles is $a$, what expression represents the measure of the other acute angle $x$?