Question

Given sin x = 5 / 7, how do you find sin 2x, cos 2x, and tan 2x?

Answer 1

20√6/49; 1/49; 20√6

Explanation:

If Sin x = 5/7,
`Cos x = sqrt(1-(5/7)^2)`
`=sqrt(24)/7=2sqrt6/7`
Then,
`Sin2x = 2Sinx*Cosx`
`=2*5/7*sqrt(24)/7`
`=20sqrt(6)/49`

Then,
`Cos2x = sqrt(1-(20sqrt(6)/49)^2)`
`=sqrt((2401-2400)/2401)`
`=1/49`

Then, since
`Tan(2x)=Sin(2x)/Cos(2x)`
`Tan(2x)=20√6`