Question

How many solutions does sin(5x) =(1/2) with the intrval (0,2pi)?

Answer 1

so the first thing you need to do is make the graph of sin(x). is looks something like this:

next you have to incorporate the fact that it is sin(5x). this means that the sine function will be finished 5 times as fast, or one cycle will be finished at 2 x pi/5. you then repeat that cycle 4 more times to get the graph of sin(5x) over the interval (0,2pi). it looks like this:


thus the answer is 10.