Use the given information to find each value. tan t=4/5,sin t <0?

A) cos2t=

B) sin2t=

C) cos t/2=

D) sin t/2=

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  • Cheech
    Lv 6
    7 years ago
    Favorite Answer

    tan t = (sin t) / (cos t)

    4/5 = (sin t) / (cos t)

    because sin t < 0, but tan t > 0, we can conclude that cos t < 0 also

    >>sin t = -4

    >>cos t = -5

    A) Using double-angle trig identities:

    cos(2t) = (cos t)^2 - (sin t)^2

    cos(2t) = (-5)^2 - (-4)^2

    >>cos(2t) = 9

    B) Using double-angle trig identities:

    sin(2t) = 2 * sin t * cos t

    sin(2t) = 2 * -4 * -5

    >>sin(2t) = 40

    C) Using half-angle trig identities:

    cos(t/2) = +/- sqrt[ (1 + cos t) / 2 ]

    cos(t/2) = +/- sqrt[ (1 - 5) / 2]

    cos(t/2) = +/- sqrt(-2)

    >>cos(t/2) = +/- i * sqrt(2)

    D) Using half-angle trig identities:

    sin(t/2) = +/- sqrt[ (1 - cos t) / 2]

    sin(t/2) = +/- sqrt[ (1 + 5) / 2]

    >>sin(t/2) = +/- sqrt(3)

    Hope this helps! :)

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