Question

Question #b922b

Answer 1

`sin2theta = 24/25`

Explanation:

`P , B , H` are perpendicular, base , hypotenuse of a right triangle.

`sin2theta =2sin thetacostheta ; sin theta =P/H = 4/5 ; P=4; H=5 :.`

By Pythagorus theorem,

`B^2=H^2-P^2 or B^2 = 5^2-4^2=9 :. B=3 ; cos theta = B/H=3/5`

`:. sin2theta =2sin thetacostheta = 2*4/5*3/5= 24/25` [Ans]

Answer 2

`sin 2t = +- 24/25`

Explanation:

`sin t = 4/5`
`cos^2 t = 1 - sin^2 t = 1 - 16/25 = 9/25`
`cos t = +- 3/5`
`sin 2t = 2sin t.cos t = 2(4/5)(+- 3/5) = +- 24/25`
There are 2 answers.
Explanation:
a. When `cos t = 3/5` --> calculator --> `t = 53^@13` -->
`2t = 106^@25` --> `sin 2t = 0.96 = 24/25`
b. When `cos t = - 3/5` --> `t = 126^@87` --> `2t = 253^@ 74` -->
`sin 2t = - 0.96 = - 24/25`