Understanding Periods of Trigonometric Functions with Different Frequencies

AI Thread Summary
The period of the function f(x) = sin 3x - (1/2)sin x is determined by the least common multiple of the individual periods of the sine functions involved. The period of sin 3x is 2π/3, while the period of sin x is 2π. Since 2π is a multiple of 2π/3, the overall period of the combined function is 2π. Understanding this concept is crucial for analyzing trigonometric functions with different frequencies. The key takeaway is that the period of the resulting function is dictated by the greater period among the components.
asatru jesus
Messages
3
Reaction score
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.
 
Mathematics news on Phys.org
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}.
 
Thread 'Video on imaginary numbers and some queries'

Thread 'Video on imaginary numbers and some queries'

Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »
Thread 'Unit Circle Double Angle Derivations'

Thread 'Unit Circle Double Angle Derivations'

Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...
View full post »

Similar threads

I Why is it important to convert angle units when using trigonometric functions?
Replies
8
Views
2K
B Can 2(sinx) be called a 'trigonometric function'?
Replies
28
Views
3K
A Can You Prove the Series Is Periodic?
Replies
33
Views
3K
I Period of a Sine Wave: Understand How to Measure in Radians
Replies
6
Views
2K
I Finding the inverse tangent of a complex number
Replies
2
Views
2K
MHB 7.8.99 find PS, VS Period, graph
Replies
7
Views
1K
I Determine ## \beta ## as a function of ##\theta## linkage
Replies
2
Views
2K
MHB Couple of hard trig questions....
Replies
1
Views
2K
B What values of m as a function of q satisfy this trigonometric equation?
Replies
5
Views
1K
MHB Fourier Series involving Hyperbolic Functions
Replies
9
Views
4K

Hot Threads

Recent Insights

Back
Top