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

Question

sec (u) = -5/2

𝜋/2 < u < 𝜋

sin(u/2) = _______

cos(u/2) = _______

tan(u/2) = _______

Answer 1

cos(u) = - 2/5 π/4 < u/2 < π/2, so u/2 in quadrant I

sin(u/2) =((1 - cosu)//2)^1/2 = ((1 + 2/5)/2)^1/2 = (7/10)^1/2

cos(u/2) = ((1 + cosu)/2)^1/2 = ((1 - 2/5)/2)^1/2 = (3/10)^1/2;

tan(u/2) = (7/10)^1/2/(3/10)^1/2 = (7/3)^1/2