3csc(2X)-5=0 What are the solutions for X and how did you find them out?

Answer 1

3 csc(2x) = 5
csc(2x) = 5/3
sin(2x) = 3/5
2x = 36.9° or 143.1°
x = 18.4° or 71.6°

Answer 2

Thanks Reiny. If a question similar to this one had 4 solutions, how would you know that it had 4 answers?

Answer 3

I cannot give a general answer to your question without seeing the actual problem

In solving trig equations, you have to consider that each trig ratio is positive in 2 different quadrants and is negative in 2 different quadrants

Usually answers are neede for the domain between 0 and 360, so the period of the trig function also has to be considered

e.g. sin (4x) = .5 would have 4 different answers between 0 and 360

Answer 4

for the example you gave i can get 37.5 deg and 7.5deg. what are the other solutions?