If csc + 5/3 and tan Ø = 3/4, find the values of the remaining trigonometric functions using a Pythagorean Identity. Show your answer.

First, decide which values represent opposite (o), adjacent (a), and hypotenuse (h) when given csc and tan:

csc = 5/3 = hypotenuse/opposite: h=5, o = 3, and a = ?

tan = 3/4 = opposite/adjacent: h = ?, o = 3, and a = 4

Combined, we get: h=5, o = 3, and a = 4

Next, plug in the values of o, a, and h:

sin = o/h → 3/5 csc = h/o → 5/3

cos = a/h → 4/5 sec = h/a → 5/4

tan = o/a → 3/4 cot = a/o → 4/3