Question

Question #49b70

Answer 1

`cos 2t = -119/169`
`tan 2t = 120/119`

Explanation:

`tan t = - 12/5`, t is in Quadrant 2.
`cos^2 t = 1/(1 + tan^2 t) = 1/(1 + 144/25) = 25/169`
`cos t = - 5/13` (cos t is negative, t in Quadrant 2)
`sin^2 t = 1 - cos^2 t = 1 - 25/169 = 144/169`
`sin t = 12/13` (sin t is positive)
`sin 2t = 2sin t.cos t = 2(12/13)(-5/13) = -120/169`
`cos 2t = 2cos^2 t - 1 = 50/169 - 1 = - 119/169`
`tan 2t = (sin 2t)/(cos 2t) = (- 120/169)(- 169/119)`
`tan 2t = 120/119`