Question

Use the information given about the angle θ, 0 ≤ θ < 2π, to find the exact value of

(a) sin (2θ)                   (b) cos (2θ)                              (c) sin (θ/2)                             (d) cos (θ/2)

sec θ = 3,     sin θ > 0

Answer 1

Step 1 :

(a)

The trigonometric function and .

Find .

Double-angle formula : .

If , then .      (Since reciprocal identity : )

Solve for .

Pythagorean identity : .

Step 2 :

(b)

Find .

Double-angle formula : .

Comments

Contd.......

Step 3 :

(c)

Find .

Half-angle formula : .

.    (Since )

Step 4 :

(d)

Find .

Half-angle formula : .

.    (Since )

Solution :

(a) The exact value of .

(b) The exact value of .

(c) The exact value of .

(d) The exact value of .