Understanding Periods of Trigonometric Functions with Different Frequencies

In summary, to find the period of f(x)= sin 3x - (1/2)sin x, we need to consider the periods of the individual functions sin 3x and sin x. The period of sin 3x is 2pi/3 and the period of sin x is 2pi. Since the period of sin 3x is smaller, we use it as the period for the entire function. This is because both functions will repeat when we reach a multiple of their separate periods, and 2pi is a multiple of 2pi/3. Therefore, the period of f(x) is 2pi/3.
  • #1
asatru jesus
3
0
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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  • #2
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?
 
  • #3
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 [tex]2\pi[/tex] is a multiple of [tex]\frac{2\pi}{3}[/tex].
 

1. What are the basic trigonometric functions?

The basic trigonometric functions are sine, cosine, and tangent. These functions are used to relate the angles of a right triangle to the lengths of its sides.

2. How do I find the value of a trigonometric function?

The value of a trigonometric function can be found by using a calculator or by using trigonometric tables. You can also use the unit circle to find the values of the functions for special angles.

3. What is the domain and range of trigonometric functions?

The domain of trigonometric functions is all real numbers, while the range depends on the specific function. Sine and cosine have a range of [-1, 1], while tangent has a range of all real numbers.

4. How can I use trigonometric functions in real-life applications?

Trigonometric functions are used in many fields, including physics, engineering, and navigation. They can be used to calculate distances, angles, and heights in real-world situations.

5. What are the inverse trigonometric functions?

The inverse trigonometric functions are the inverse of the basic trigonometric functions. They are denoted as sin^-1, cos^-1, and tan^-1 and are used to find the angle that would produce a given value for a trigonometric function.

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