how to solve sin u/2 cos u/2 and tan u/2

Question

sin u= 7/25,    pi/2 is less than or equal to u is less than or equal to pi

 

Find the exact values of 

sin(u/2),

 cos(u/2), 

tan(u/2)

 using the half-angle formulas.

Answer 1

Step 1:

The trigonometric function is

Since lies in quadrant II then is also lies in quadrant II.

Pythagorean theorem,

Find .

Using half - angles formulas: .

Substitute in above formula.

Step 2:

Find .

Using half - angles formulas: .

Substitute in above formula.

Step 3:

Find .

Using half - angles formulas: .

Substitute in above formula.

Solution :