Quandaries
and Queries 

WHAT IS THE PERIOD OF SIN(X)+COS(X)? PLEASE EXPLAIN WITH A GRAPH. 

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 

