Question

How would you use the half-angle formula to find the exact values of `tan 195`degrees?

Answer 1

Use the trig identity: `tan 2a = (2tan a)/(1 - tan^2 a)`
`tan 2(195) = tan 390 = tan (30 + 360) = tan 30 = sqrt3/3`
Call t = tan 195.
`sqrt3/3(1 - t^2) = 2t --> (1 - t^2) = 2sqrt3t`

-> `t^2 + 2sqrt3 - 1 = 0`

`D = d^2 = 12 + 4 = 16 --> d = +- 4`

`t = tan 195 = (- 2sqr3)/2 + 4/2 = (2 - sqrt3)`

`t = tan 195 = - sqrt3 - 4 = -5.414` Rejected because arc 195 is on Quadrant III. Its tan must be positive.