cos u 941 0 u 2 Find the exact values of sinu2 cosu2 and

cos u = 9/41, 0 < u < /2 Find the exact values of sin(u/2), cos(u/2), and tan(u/2) using the half-angle formulas.

Solution

cos u = 9/41, 0 < u < /2

ie u lies in Ist quadrant.

i) from cos u = 1- 2*sin²( u/2)

sin(u/2) = ( 1- cosu / 2)^1/2

= [( 1- 9/41) / 2)^1/2

= 0.6246

ii) from cos u = 2*cos² ( u/2) - 1

cos(u/2) = ( cos u+1 / 2)^1/2

= [( 9/41 ) + 1) / 2)^1/2

= 0.780

iii) tan(u/2) = sin(u/2) / cos (u/2)

= 0.8007