Question

Find sin2a if sina=3/5 and a is in quadrant 2

Answer 1

sin(a)=
`(3)/(5)`

To find sin(2a) = 2*sin(a)*cos(a), we ned to find cos(a)

We know that,

sin²(a) + cos²(a) = 1

cos(a) =
`√(( 1- sin^2 a))`

cos(a) =
`\sqrt{1- ( (3)/(5) )^2} = \sqrt{1- (9)/(25)} = \sqrt{ (16)/(25)} = (4)/(5)`

Thus, cos(a) = +-
`(4)/(5)`

We know a is in second quadrant and thus cos(a) is -
`(4)/(5)` because cosine is always negative in the second quadrant.

Therefore,

sin(2a) = 2*sin(a)*cos(a) =
`2* (3)/(5) * (-4)/(5) = (-24)/(25)`