Understanding Periods of Trigonometric Functions with Different Frequencies

asatru jesus
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f(x)= sin 3x - (1/2)sin x, find the period.

i know the period for sin 3x is 2pi/3 and the period of sin x is 2pi but how do you subtract these? I totally forget how to do this! I mean i could find the answer with any graphing program but i want to know how to do this type of problem.
 
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asatru jesus said:
f(x)= sin 3x - (1/2)sin x, find the period.

i know the period for sin 3x is 2pi/3 and the period of sin x is 2pi but how do you subtract these? I totally forget how to do this! I mean i could find the answer with any graphing program but i want to know how to do this type of problem.

Go with the greater value (period). Can you see why?
 
Why subtract them? The two functions will both repeat when you reach the least common multiple of their separate periods. Here, it should be obvious that 2\pi is a multiple of \frac{2\pi}{3}.
 

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