Sin 2 u , Cos 2 u , Tan 2 u , Sin u/2 , Cos u/2 , Tan u/2

Question

Given that csc u= 17/15 and 0 < u < pi/2 , use double angle or half angle formulas to find the following

Answer 1

cscu = 17/15

sinu = 1/cscu = 15/17

cosu = -8/17 (17^2 = 15^2 + 8^2)

sin2u=2sinucosu = 2(15/17)(8/17) = 240/289 = about 0.83

cos2u = cos^2u - sin^2u = (8/17)^2 - (15/17)^2 = -161/289 = about -0.67

tan2u = sin2u/cos2u = 240/-161 = -240/161 = - about -1.49

u= about 62 degrees

u/2 = about 31 degrees

sin31= 0.51

cos31 = 0.86

tan31 = 0..59

u is in quadrant I u=62

2u is in quadrant II, 2u=124

u/2 is in quadrant I u/2=31