if sin where defined=1/5 and where defined is in quadrant I find the exact value of sin2 where defined

Answer 1

make a diagram and use Pythagoras to find the third side x
x^2 + 1^2 = 5^2
x = sqrt(24)

so cos(theta)= sqrt(24)/5

sin(2theta) = 2sin(theta)cos(theta)
= 2(1/5)(sqrt(24)/5)
= 2sqrt(24)/25
or
= 4sqrt(6)/25