Question

If sin(θ)=4/5​ and θ is in the first quadrant, find cos(2θ) A) 7/25​ B) 24/25​ C) −7​/25D) −9​/25

Answer 1

C

Explanation:

using the identity

cos2θ = 1 - 2sin²θ

given sinθ =
`(4)/(5)` , then

cos2θ

= 1 - 2(
`(4)/(5)` )²

= 1 - 2 (
`(16)/(25)` )

= 1 -
`(32)/(25)`

=
`(25)/(25)` -
`(32)/(25)`

= -
`(7)/(25)` → C