# Why are there 3 solutions in this trigonometric equation $sin\theta = 0$

my question is Why are there 3 solutions in this trigonometric equation $$sin\theta = 0$$? I thought since the range for the angle is between 0 and 360 it has 2 solutions? I tried and I have got 2 solutions which are 0, and 180 but apparently there is 1 more solution. Can someone please explain this and if you can, also tell me what do I do if I obtain a negative angle? For example in this equation $$tan(\theta-50)=-1.7$$, I solved and got a negative angle, how do I proceed to the next step? Please help Thank you!

• Where do you need your solutions to exist? Without restriction, the equation $\;\sin\theta=0\;$ has infinite solutions: $\;\theta=k\pi\;$ , for any integer $\;k\;$ . – DonAntonio Nov 10 '18 at 1:47
• There are only $2$ solutions in $[0,360)$ If you increase the interval you can get more. – Doug M Nov 10 '18 at 1:50
• In $[0^{\circ}, 360^{\circ}]$ there are 3 solutions: $0^{\circ}, 180^{\circ}, 360^{\circ}$ – Jaroslaw Matlak Nov 10 '18 at 1:51
• $\arctan(x)$ is defined to be in $(-\frac {\pi}{2}, \frac {\pi}{2})$ if you want an answer in $[0,\frac{\pi}{2})\cup(\frac {\pi}{2},\pi)$ you can add $\pi$ to your result. – Doug M Nov 10 '18 at 1:52
• @JaroslawMatlak why 360? i thought only 0, and 180? – Fred Weasley Nov 10 '18 at 2:22