Using half angle formulas

Question

Use the given conditions.

cos(u) = 7/25,    0 < u < 𝜋/2

what is sin(u/2)

cos(u/2)

tan(u/2)

Answer 1

We are in quadrant 1, where all trigonometric values, and the trigonometric values of all half-angles, is positive

sin(u/2) = √((1-cos(u))/2) = √((1-7/25)/2) = √((18/25)/2) = √9/25)= 3/5

cos(u/2) = √((1+cos(u))/2) = √((1+7/25)/2) = √((32/25)/2) = √16/25)= 4/5 (As a check of sin and cos, think of the 3-4-5 right triangle)

tan(u/2) = sin(u/2)/cos(u/2) = 3/5/(4/5) = 3/4