Question 1133868
sin(x) = 0 when x = 0 or 180 or 360 or -180 or -360, etc.


the general formula would be sin(x) = 0  when x = 0 plus or minus k * 180, where k = any positive integer.


when you're dealing with radians, the general formula would be sin(x) = 0 when x = 0 plus or minus k * pi.


that's because pi radians is equal to 180 degees.


the conversion factor is degrees = radians * 180 / pi and radians = degrees * pi / 180.


so 180 degrees * pi / 180 = pi radians and pi radians * 180 / pi = 180 degrees.


your interval of interest is -pi/2 radians to 3pi/2 radians.


-pi/2 radians * 180 / pi = -90 degrees.


3pi/2 radians * 180 / pi = 270 degrees.


your interval in radians is -pi/2 to 3pi/2 radians.


you interval in degrees is - 90 to 270 degrees.


in degrees, the general formula of sin(x) = 0 when x = 0 plus or minus 180 degrees will get you x = 0, 180, 360, 540, ... and x = 0, -180, -360, -540, ... .


0 and 180 are in the interval between -90 and 270 degrees, so they have to be your answer.


in radians, the general formula of sin(x) = 0 when x = 0 plus or minus pi radians will, get you x = 0, pi, 2pi, 3pi, .... and x = 0, -pi, -2pi, -3pi, ... .


in the interval between -pi/2 and 3pi/2, x = 0 and pi fits.


in degrees, x is equal to 0 or 180 degrees.
in radians, x is equal to 0 or pi radians.


the first graph shows you this in degrees.


<img src = "http://theo.x10hosting.com/2019/020203.jpg" alt="$$$" >


the second graph shows you this in radians.


<img src = "http://theo.x10hosting.com/2019/020204.jpg" alt="$$$" >