If sina = 3/5, find the value of cos(a) and sin2a

Given that sin(a) = 3/5

We need to
find cos(a).

First we will use trigonometric identities to find
cos(a).

We know that:

sin^2 a + cos^2 a
= 1

==> cos(a) = sqrt( 1- sin^2
a)

==> cos(a) = +-sqrt( 1- (3/5)^2 = sqrt( 1- 9/25) = sqrt
16/25 = 4/5

Then cos(a) = +- 4/5

Now we
will calculate sin2a

==> we know that sin2a =
2sina*cosa

Now we will substitute
:

==> sin2a = 2*3/5* +-4/5 =
+-24/25

==> sin2a =
+-24/25

Then cosa = +- 4/5 and sin2a = +-
24/25