Can find the exact value of each of the remaining trigonometric functions of θ if sin θ=4/5, 90*<θ<180* ?

Question

cos θ =

csc θ =

tan θ =

cot θ =

Answer 1

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Answer 2

sinx = 4/5 where x is in the 3rd quadrant

it's a 3-4-5 right triangle. 25 =9 +16

pythagorean theorem applies, with hypotenuse = 5, sides 3 and 4

3^2+ 4^2 = 5^2

cosx = -3/5

cscx = 1/sinx = 5/4

secx = 1/cosx = -5/3

in the 3rd quadrant, all trig functions are negative, except sines and cosecants

tanx = sinx/cosx = -4/3

cotx = cosx/sinx = -3/4