pre cal

assume the angle is in the first quadrant, and sin theta equals 1/5. what is sin 2 theta?

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  1. sin(theta)=1/5

    cos(theta)=sqroot[1-sin(teta)^2]

    cos(theta)=sqroot[1-(1/5)^2]

    cos(theta)=sqroot(1-1/25)

    cos(theta)=sqroot(25/25-1/25)

    cos(theta)=sqroot(24/25)

    cos(theta)=sqroot(6*4/25)

    cos(theta)=sqroot(6*2^2/5^2)

    cos(theta)=(2/5)*sqroot(6)

    sin(2theta)=2*sin(theta)*cos(theta)

    sin(2theta)=2*(1/5)*(2/5)sqroot(6)

    sin(2theta)=(4/25)*sqroot(6)

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