The trigonometric equation is in the interval .

and lies in third quadrant.

From Pythagorean theorem,

Since lies in third quadrant, and are negative.

.

.

(a)

Find .

Use Double-angle formula: .

.

Substitute and .

.

(b)

Find .

Use Double-angle formula: .

.

Substitute and .

.

(c)

Find .

Use Half-angle formula: .

Substitute .

.

Where lies in second quadrant, since lies in third quadrant.

Therefore, is positive.

.

(d)

Find .

Use Half-angle formula: .

Substitute .

Where lies in second quadrant, since lies in third quadrant.

Therefore, is negative.

.

(a) .

(b) .

(c) .

(d) .