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

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We have sin a = 3/5

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

=> sqrt (1 - 9/25)

=> sqrt (16/25)

=> 4/5 or -4/5 based on the value of a

sin 2a = 2*sin a*cos a

=> 2*3/5*4/5

=> 24/25 or -24/25 base on the angle a

**The value of cos a can be 4/5 or -4/5 and sin 2a = 24/25 or -24/25 based on which quadrant a is in.**

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**