How Can I Quickly Find the Period of a Trigonometric Function Without Graphing?

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SUMMARY

The period of the trigonometric function x = (2/5)cos(t) + (1/5)sin(t) is determined to be 2π. Both components, (2/5)cos(t) and (1/5)sin(t), have individual periods of 2π. The least common multiple of these periods is also 2π, confirming that the overall period of the function is 2π. This method allows for quick determination of the period without the need for graphing.

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x = (2/5)cos(t) + (1/5)sin(t)

by graphing this, I found the period to be 2*pi.

My concern is, when taking an exam I won't have time to bother with graphing or I'll get slammed with a weird graph and panic and get stuck.

I'm pretty sure there is a way to find the period quickly without graphing? I am running into this problem in my dyamical systems class and my calculus and trig are sooooooooo rusty.

Thanks,
Candio
 
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The function is made out of two parts, added together. What is the period of the first part? What is the period of the second part? What is the least common multiple of that (e.g. if the period for one is 3 and for the other one 4, then it will be 12; but if it is 3 and 6 then it will be 6).
 
Ha! Thanks. You're the best :)

lets see

period 2/5.cos(t) = 2pi
1/5.sin(t) = 2pi

least common multiple = 2pi

sweet
 

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