find the exact values of sin (u/2), cos (u/2), and tan (u/2) using the half - angle formulas.

Question

(a) Determine the quadrant in which u/2 lies, and (b) find the exact values of sin (u/2), cos (u/2), and tan (u/2) using the half - angle formulas.

cos u = 7/25,       0 < u < π/2

Answer 1

Step 1:

(a)

The trigonometric function is , .

Since lies in quadrant I, then is also lies in quadrant I.

Step 2:

(b)

Find .

Using half - angles formulas : .

Substitute in above formula.

.

Step 3:

Find .

Using half - angles formulas : .

Substitute in above formula.

.

Step 4:

Find .

Using half - angles formulas : .

From Pythagorean theorem, .

Substitute and in above formula.

.

Solution :

(a) lies in quadrant I.

(b) , and .