Understanding Periods of Trigonometric Functions with Different Frequencies

[asatru jesus]

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.

 

[amcavoy]

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?

 

[HallsofIvy]

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 $$\frac{2\pi}{3}$$.