Trig Question

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Given that tan x= -3/4 and x is in the second quadrant. Find sin 2x, cos 2x, and tan 2x (Exact, no decimals).

Please show step-by-step, thank you!

  • Trig Question -

    construct a triangle in quad II with x=-4 and y = 3
    since tanĂ˜ = y/x or opposite/adjacent
    so r^2 = (-4)^2 + 3^2
    r = 5
    sinx = 3/5 and cosx = -4/5

    you have to know that
    sin 2x = 2sinxcosx = 2(3/5)(-4/5) = -24/25
    cos 2x = cos^2 x - sin^2 x = 16/25 - 9/25 = 7/25
    tan 2x = sin 2x/ cos 2x = (-24/25) / (7/25) = -24/7

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