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

  • Thread starter Somefantastik
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In summary, the function x = (2/5)cos(t) + (1/5)sin(t) has a period of 2pi when graphed. However, there is a way to find the period quickly without graphing by determining the period of each individual part and finding the least common multiple. In this case, the least common multiple is 2pi.
  • #1
Somefantastik
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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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  • #2
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).
 
  • #3
Ha! Thanks. You're the best :)

lets see

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

least common multiple = 2pi

sweet
 

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

What is the definition of period in a function?

The period of a function is the length of the interval over which the function repeats its values. In other words, it is the distance between two consecutive points on the function's graph where the function has the same value.

How do you find the period of a trigonometric function?

To find the period of a trigonometric function, you need to first identify the coefficient of the independent variable in the function. This coefficient is known as the "b" value. The period of the function is then given by 2π/|b|.

Can the period of a function be negative?

No, the period of a function cannot be negative. It is always a positive value that represents the distance between two consecutive points on the function's graph where the function has the same value.

How does the graph of a function change when the period is altered?

Changing the period of a function affects the frequency of its repetitions. If the period is increased, the graph will stretch horizontally and if the period is decreased, the graph will compress horizontally.

Is there a formula for finding the period of any function?

No, there is not a single formula that can be used to find the period of any function. The method for finding the period may vary depending on the type of function, such as trigonometric, exponential, or polynomial.

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