Question

Please help complete the statement

Answer 1

sin2θ = -
`(24)/(25)`

Explanation:

Given

cosθ =
`(3)/(5)` =
`(adjacent)/(hypotenuse)` and in fourth quadrant

Then this is a 3- 4- 5 triangle with opposite side = 4

sinθ < 0 in fourth quadrant, then

sinθ = -
`(opposite)/(hypotenuse)` = -
`(4)/(5)`

Using the double angle identity for sine

sin2θ = 2sinθcosθ

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