Using the Half-Angle Formulas


Find the function values in Exercises 47–50.


cos² 5π/12

In Exercises 39–42, express the given quantity in terms of sin x and cos x.

cos (3π/2 + x)

What happens if you take B = 2π in the addition formulas? Do the results agree with something you already know?

Evaluate cos (11π/12) as cos (π/4 + 2π/3).

Evaluate sin (5π/12).

Using the Half-Angle Formulas

Find the function values in Exercises 47–50.

sin² 3π/8

Solving Trigonometric Equations

For Exercises 51–54, solve for the angle θ, where 0 ≤ θ ≤ 2π.

sin² θ = cos² θ

The law of sines The law of sines says that if a, b, and c are the sides opposite the angles A, B, and C in a triangle, then

(sin A) / a = (sin B) / b = (sin C) / c

Use the accompanying figures and the identity sin (π − θ) = sin θ, if required, to derive the law.

Simplify the expression.

$\tan^2\theta-\sec^2\theta+1$