Find the exact value of tan(θ/2) given that..

Question

Find the exact value of tan(θ/2) given that cosθ=-8/17 and θ is in Q2.

Answer 1

cos(theta) =-8/17 = adjacent side over hypotenuse

theta = about 180-61.9 = 118.1 degrees, theta/2 = a little less than 60, tan60 = sq3 =about 1.7

opposite side^2 = 17^2 - 8^2 = 289-64=225

opposite side = 15

tan(theta) = 15/-8 = -15/8

tan(theta/2) = sqr(1-cos(theta))/1+cos(theta) = sqr((25/9) = 5/3

(ignore the negative square root as theta/2 is in the 1st quadrant

tan(theta/2) = exactly 5/3, using the half angle identity formula

= about 1.7