Thread: Find cos x and csc x

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

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


PLEASE HELP?

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.

--------------
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.