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# 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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- CheechLv 67 years agoFavorite 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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