2. Trigonometric Functions on Right Triangles

In Exercises 9–16, use the given triangles to evaluate each expression. If necessary, express the value without a square root in the denominator by rationalizing the denominator.

cot 𝜋/3

In Exercises 9–16, use the given triangles to evaluate each expression. If necessary, express the value without a square root in the denominator by rationalizing the denominator.

sin 𝜋/4 - cos 𝜋/4

In Exercises 9–16, use the given triangles to evaluate each expression. If necessary, express the value without a square root in the denominator by rationalizing the denominator.

tan 𝜋/4 + csc 𝜋/6

In Exercises 63–68, find the exact value of each expression. Do not use a calculator.tan 𝜋/3 - ___1___ 2 sec 𝜋/6

In Exercises 63–68, find the exact value of each expression. Do not use a calculator.1 + sin² 40° + sin² 50°

In Exercises 63–68, find the exact value of each expression. Do not use a calculator.csc 37° sec 53° - tan 53° cot 37°

In Exercises 63–68, find the exact value of each expression. Do not use a calculator.cos 12° sin 78° + cos 78° sin 12°

In Exercises 69–70, express the exact value of each function as a single fraction. Do not use a calculator.If f(θ) = 2 cos θ - cos 2θ, find f(𝜋/6).

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.(-4, 3)

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)

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)

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.(-1, -3)

In Exercises 9–16, evaluate the trigonometric function at the quadrantal angle, or state that the expression is undefined.tan 𝜋

In Exercises 9–16, evaluate the trigonometric function at the quadrantal angle, or state that the expression is undefined.csc 𝜋

In Exercises 9–16, evaluate the trigonometric function at the quadrantal angle, or state that the expression is undefined.cos 3𝜋2