2. Trigonometric Functions on Right Triangles

Use the triangle to find each of the six trigonometric functions of θ.

In Exercises 23–26, find the exact value of each expression. Do not use a calculator.cos² 𝜋 - tan² 𝜋 4 4

In Exercises 23–26, find the exact value of each expression. Do not use a calculator.cos 2𝜋 sec 2𝜋9 9

In Exercises 37–38, a point on the terminal side of angle θ is given. Find the exact value of each of the six trigonometric functions of θ, or state that the function is undefined.(0, -1)

If sin θ = a and cos θ = b, represent each of the following in terms of a and b.tan θ - sec θ

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

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

Sketch an angle θ in standard position such that θ has the least positive measure, and the given point is on the terminal side of θ. Then find the values of the six trigonometric functions for each angle. Rationalize denominators when applicable. See Examples 1, 2, and 4. (―12 , ―5)

Sketch an angle θ in standard position such that θ has the least positive measure, and the given point is on the terminal side of θ. Then find the values of the six trigonometric functions for each angle. Rationalize denominators when applicable. See Examples 1, 2, and 4. (―8 , 15)

Sketch an angle θ in standard position such that θ has the least positive measure, and the given point is on the terminal side of θ. Then find the values of the six trigonometric functions for each angle. Rationalize denominators when applicable. See Examples 1, 2, and 4. (0, ―3)

Sketch an angle θ in standard position such that θ has the least positive measure, and the given point is on the terminal side of θ. Then find the values of the six trigonometric functions for each angle. Rationalize denominators when applicable. See Examples 1, 2, and 4. (―2√3 , 2)

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

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.) IV , x/y

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.) IV , x/r

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.) II , y/x