If sin x = -3/5 and x is in the 3rd quedrant, find cos x ?

sine = opp / hyp = -3/5

So,

opp = -3

hyp = 5 ---always positive.

cos = adj / hyp.

We need to find the adjacent side.

By Pythagorean theorem,

(hyp)^2 = (opp)^2 +(adj)^2

5^2 = (-3)^2 +(adj)^2

25 = 9 +(adj)^2

25 -9 = (adj)^2

16 = (adj)^2

+,-4 = adj

Since angle x is in the 3rd quadrant (to the left of the y-axis), then "x" or adj is negative.

Hence, adj = -4

Therefore, cos x = adj / hyp = -4/5 ----answer.

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If cos x = 5/13 and x is in the fth quadrant, find csc x?

What is fth?

Anyway, follow the example above and you should get the answer.