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

  • trigonometry -

    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
    = 4sqrt(6)/25

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