If csc=5/4 and cos< 0, find the values of the other trigonometric functions?

Answer 1

csc 5/4 sin is the reciprocal of csc and so
sin=4/5
if sin=4/5 the hyp is 5 and the opposite side is 4
so the adjacent side is 3/5 so
cos=-3/5
tan=-4/3
sec=-5/3
cot=-3/4

Answer 2

Draw a triangle to help figure it out. Cosine is negative in the second and third quadrants, and sine (and thus csc) is positive in the first and second, so your triangle will be in the second quadrant.

Since cosecant is H/O, you can use the Pythagorean theorem to get your third side and get the rest of the trig functions everyone's been giving you. :-P

Answer 3

csc(x) = (5/4)
1/(sin(x)) = (5/4)
sin(x) = (4/5)

4^2 + a^2 = 5^2
16 + a^2 = 25
a^2 = 9
a = 3 or -3

cos(x) = (-3/5)
sin(x) = (4/5)
tan(x) = (-3/4)
cot(x) = (-4/3)
sec(x) = (-5/3)