Question

If tan A 3/4 find the value of: sin2A​

Answer 1

24/25

Explanation:

use tan^-1 to find the angle

tan^-1(3/4)=36.86989765°

A =36.86989765°

2A= 2×36.86989765

=73.73979529°

sin2A>>>>sin(73.73979529°)

=24/25 or 0.96

Answer 2

sin2A =
`(24)/(25)`

Explanation:

using the identity

sin2A = 2sinAcosA

given

tan2A =
`(3)/(4)` =
`(opposite)/(adjacent)`

then this is a 3- 4- 5 right triangle with

hypotenuse = 5, opposite = 3 , adjacent = 4 , then

sinA =
`(opposite)/(hypotenuse)` =
`(3)/(5)` and cosA =
`(adjacent)/(hypotenuse)` =
`(4)/(5)`

Then

sin2A = 2 ×
`(3)/(5)` ×
`(4)/(5)` =
`(2(3)(4))/(5(5))` =
`(24)/(25)`