Hi,

The periods of sin(x) and cos(x) are both 360^o so sin(x) + cos(x) repeats on any interval of length 360^o. Thus 360^o is a period of sin(x) + cos(x). The question is then, is 360^o the period of sin + cos(x)? That is, is 360^o the length of the shortest interval on which sin + cos(x) repeats? This is where a graph is useful.

I plotted sin(x) + cos(x) for x from -360^o to 720^o

From the graph you can see that there is a repeat on intervals of length 360^o but no shorter interval where the graph repeats. Thus the period of sin + cos(x) is 360^o.

Penny

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