2. Trigonometric Functions on Right Triangles

Find the indicated function value. If it is undefined, say so. See Example 4. sin 90°

Use identities to solve each of the following. Rationalize denominators when applicable. See Examples 5–7. Find cot θ , given that csc θ = ―1.45 and θ is in quadrant III.

Concept Check Suppose that the point (x, y) is in the indicated quadrant. Determine whether the given ratio is positive or negative. Recall that r = √(x² + y²) .(Hint: Drawing a sketch may help.) III , y/r

Solve each problem. See Examples 1 and 2. Distance between Two Ships Two ships leave a port at the same time. The first ship sails on a bearing of 52° at 17 knots and the second on a bearing of 322° at 22 knots. How far apart are they after 2.5 hr?

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

sec θ = ―√5 , and θ is in quadrant II

In Exercises 1–8, use the Pythagorean Theorem to find the length of the missing side of each right triangle. Then find the value of each of the six trigonometric functions of θ.

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. (5, -5)

Find the indicated function value. If it is undefined, say so. See Example 4. sec 180°

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. tan θ

Concept Check Find a solution for each equation. sec(2θ + 6°) cos(5θ + 3°) = 1

Find the six trigonometric function values for each angle. Rationalize denominators when applicable.

In Exercises 23–34, find the exact value of each of the remaining trigonometric functions of θ. sec θ = -3, tan θ > 0