When sinx=0, what does x equal?

#sinx# is known as a periodic function that oscillates at regular intervals.

It crosses the x-axis (i.e. it is #0#) at #x = 0, pi,# and #2pi# in the domain #[0,2pi]#, and continues to cross the x-axis at every integer multiple of #pi#.

graph{sinx [-10, 10, -5, 5]}

And if you click on the graph, you get:

So, whenever #sinx = 0#, we have that:

#color(blue)(x = pi pm kpi)# for all #k# in the set of integers.

That is, if #k = 0, 1, 2, . . . , N#, where #N# is some arbitrarily large integer, then #sinx = 0# for #x = 0, pmpi, pm2pi, . . . , pm2Npi#.

If you know that #sinx = 0#, t
Then you need to use a process called 'arcsin'.
It might be shown as "arcs" or "asin" or similar.

This is shown as #sin^-1# on many calculators and is not to be confused with #1/sin# which is the same as #"cosec"#

To find which angle(s) will have a sine value of #0#.

Depending on what type of calculator you have you key in one of the following:

• #"shift" sin 0 =# and you get the answer #0°#

• #0 " shift" sin# the display will read #0#

Any angle which is a multiple of #180°# will also have a sin value of #0#