Question

given sin theta =-3/5 and csc theta =-5/3 in quadrant 3, how do I find the value of other trigonometric functions using a Pythagorean identity?

Answer 1

make a triangle attt 3rd quadrant \[\rm sin = \frac{ opposite }{ hypotenuse }~~~~ \cos = \frac{ adjacent }{ hypotenuse } ~~\tan= \frac{ opposite }{ adjacent }\]

Answer 2

sin is opposite over hypotenuse
so apply Pythagorean theorem to find 3rd side of right triangle
a^2+b^2 =c^2