Question

Question #36b27

Answer 1

`120/169`

Explanation:

`tan t = 5/12` --> `cot t = 12/5`
Use trig identity:
`sin^2 t = 1/(1 + cot^2 t)\sin^2 t = 1/(1 + 144/25) = 25/169`
`sin t = +- 5/13`
Since t is in Quadrant 3, there for, sin t is negative
`sin t = - 5/13`.
Find cos t.
`co^2 t = 1 - sin^2 t = 1 - 25/169 = 122/169`
`cos t = - 12/13` (t in Quadrant III)
`sin 2t = 2sin t.cos t = 2(-5/13)(-12/13) = 120/169`