Question

If sin (x) =2/5 and tan(x) > 0, what is sin(2x)?

Answer 1

sin2x =
`(4√(21) )/(25)`

Explanation:

Given sinx =
`(2)/(5)` =
`(opposite)/(hypotenuse)`

Then the third side, the adjacent is found using Pythagoras' identity, that is

adj² + opp² = hyp²

adj² + 2² = 5²

adj² + 4 = 25 ( subtract 4 from both sides )

adj² = 21 ( take the square root of both sides )

adj =
`√(21)` , then

cosx =
`(adj)/(hyp)` =
`(√(21) )/(5)`

Using the double angle identity

sin2x = 2sinxcosx

= 2 ×
`(2)/(5)` ×
`(√(21) )/(5)`

=
`(4√(21) )/(25)`