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# Given csc(theta)=5/4, determine tan(theta) if (pi/2) is < or equal to (theta) < or equal to (pi)?

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- Wayne DeguManLv 74 weeks agoFavourite answer
cosecθ = 1/sinθ

so, 1/sinθ = 5/4

i.e. sinθ = 4/5

As we have a 3, 4, 5 triangle we have that cosθ = -3/5

Note: negative, as cosθ < 0 in Qii

And sinθ/cosθ = tanθ = (4/5)/(-3/5)

i.e. tanθ = -4/3

:)>

- cosmoLv 74 weeks ago
csc(theta) = 5/4

sin(theta) = 4/5

cos(theta) = sqrt(1 - (4/5)^2) = sqrt(1 - 16/25) = sqrt(9/25) = + or - 3/5

If theta is in the second quadrant, then cos(theta) = - 3/5

tan(theta) = sin/cos = (4/5)/(-3/5) = -4/3

- 4 weeks ago
csc(t)^2 - cot(t)^2 = 1

cot(t) = 1/tan(t)

(5/4)^2 - cot(t)^2 = 1

(5/4)^2 - 1 = cot(t)^2

25/16 - 16/16 = cot(t)^2

9/16 = cot(t)^2

16/9 = tan(t)^2

+/- 4/3 = tan(t)

You're in Q2, so is tan(t) positive or negative? You have a 1-in-2 shot here, just by guessing

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