# What is sin(x/4) of my graph?

I am having problems interpreting what sin(x/4) is . I have done a graph for sin(X) and sin(x/4) from 0 to 12pi on the x axis,and this makes the x axis go to about 37.699111 radians. The sin(x) goes from 0 up to +1 on the y axis, this is about 90 degrees. Then it goes back through the x axis at about 3, then down to y-1, this is about 270 degrees. Then it goes up to about 6.283185307 radians on the x axis. So does this mean that the value of x in sin(x) = 360 degrees or 6.283185307 or 2pi.

This is were I am having the problem. The sin(x/4) aslo goes from 0 up to yx1 then it comes down through the x axis at about 13 and down to y-1, the same as sin(x). Then it goes right up to about 25.13261228 radians on the x axis, and this covers four cycles of sin(x). Does this mean that sin(x/4) is four times more then sin(x), which would be about 1440 degrees or about 25.132699111 radians or does this mean you are dividing sin(x) by four and this would be 90 degrees or about 1.570796327 radians. Or none of them are right. If not what would it be, So the question is what is sin(x/4) in radians. And what would sin(x) + sin(x/4) in radians.

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#### Solution Preview

Hi; I think you have done a very good job.Actually,the function of

<br>sin(x) is a typical periodic function with period 2*pi.That means for any x,we always get the equation sin(x)=sin(x+2*pi*n),and n is any intergal. This can explicitly explain why the graph of sin(x) you get will repeat the value when x is larger ...

#### Solution Summary

The graph of sin(x/4) is exlained.