maximum of sin θ

[xxMsJojoxx]

Why is the maximum of sin θ ?

I understand that it is , because when I graph y=sin θ on a graphing calculator, that is the maximum. But I don't understand this part, . Why is this part of the maximum?

 

[Dr.Peterson]

Why is the maximum of sin θ View attachment 22641?

I understand that it is View attachment 22642, because when I graph y=sin θ on a graphing calculator, that is the maximum. But I don't understand this part, View attachment 22643. Why is this part of the maximum?

Again, it's because the sine is periodic. It reaches the peak once in every cycle.

It has to be stated, though, the k is an integer; and in your form with the plus-or-minus, it only has to be a non-negative integer.