3. Unit Circle

Find one solution for each equation. Assume all angles involved are acute angles. See Example 3.sec(3β + 10°) = csc(β + 8°)

Find one solution for each equation. Assume all angles involved are acute angles. See Example 3.csc(β + 40°) = sec(β - 20°)

In Exercises 41–43, find the exact value of each of the remaining trigonometric functions of θ.cos θ = 2/5, sin θ < 0

Determine whether each statement is true or false. See Example 4.tan 28° ≤ tan 40°

Determine whether each statement is true or false. See Example 4.cos 28° < sin 28°(Hint: sin 28° = cos 62°)

Determine whether each statement is true or false. See Example 4.cot 30° < tan 40°

Determine whether each statement is true or false. See Example 4.csc 20° < csc 30°

Give the exact value of each expression. See Example 5.tan 30°

Give the exact value of each expression. See Example 5.sin 30°

Give the exact value of each expression. See Example 5.cos 30°

Give the exact value of each expression. See Example 5.sec 45°

Give the exact value of each expression. See Example 5.cot 45°

Give the exact value of each expression. See Example 5.csc 60°

Concept Check Work each problem.Find the equation of the line that passes through the origin and makes a 30° angle with the x-axis.

Concept Check Work each problem.What angle does the line y = √3x make with the positive x-axis?