Pre-Calculus, 9th edition

 PAGE: 491 SET: Exercises PROBLEM: 7

The trigonometric equation is in the interval .

.

From Pythagorean theorem,

The square of the hypotenuse is equal to sum the squares of the other two sides.

.

In first quadrant, the six trigonometric functions are positive.

.

(a)

Find .

Use Double-angle formula: .

Substitute and .

.

(b)

Find .

Use Double-angle formula: .

Substitute and .

.

(c)

Find .

Use Half-angle formula: .

Substitute .

.

(d)

Find .

Use Half-angle formula: .

Substitute .

.

(a) .

(b) .

(c) .

(d) .

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