Question

Given: cosθ = 20/29
Find: sin2θ

Answer 1

0.998

Explanation:

cos θ = 20/29

sin θ = √29² - 20² / 29 = 21 / 29

sin 2θ = 2 sinθ cosθ = 2 x 21/29 x 20/29 = 0.998

Answer 2

Sin2θ =
`(840)/(841)`

Explanation:

Let's take a right angle triangle ABC.

From triangle ABC,

Cosθ =
`(AB)/(BC) = (20)/(29)` (Given)

By Pythagoras theorem,

`(AC)^(2) + (AB)^(2) = (BC)^(2)`

`(AC)^(2) = (BC)^(2) - (AB)^(2)`

`(AC)^(2) = 29^(2) -20^(2)`

`(AC)^(2) = 841 - 400 = 441\\AC = √(441) = 21`

So, Sinθ =
`(AC)/(BC) = (21)/(29)`

Sin2θ = 2 x Sinθ x Cosθ

=
`2*(21)/(29) *(20)/(29)`

=
`(840)/(841)`