Periods of Powers of Trigonometric Functions

Click For Summary

Homework Help Overview

The discussion revolves around determining the period of a complex trigonometric function involving squared sine and cosine terms, as well as linear sine and cosine terms. The function is presented in the form f(x) = a*sin(b*x)^2 + c*cos(d*x)^2 + e*sin(f*x) + g*cos(h*x).

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to find a method for determining the period of the function, expressing uncertainty due to the presence of exponents. Another participant suggests using arbitrary values for the constants and graphing the function as a potential approach. Additionally, one participant mentions the use of trigonometric identities, specifically half-angle identities, as a possible direction.

Discussion Status

The discussion is ongoing, with participants exploring different approaches and sharing insights. Some guidance has been offered regarding the use of trigonometric identities, and there is an acknowledgment of the potential utility of graphing the function to derive periodicity.

Contextual Notes

Participants are working within the constraints of a homework problem, and there is an emphasis on not providing direct solutions. The original poster has requested guidance without explicit instructions.

Shaggy16
Messages
7
Reaction score
0

Homework Statement


Is there a way to determine the period of a function like f(x) = a*sin(b*x)^2 + c*cos(d*x)^2 + e*sin(f*x) + g*cos(h*x)?


Homework Equations





The Attempt at a Solution


I know how to find the periods of sines, cosines, and arbitrary sums of the two, but the introduction of exponents has me at a complete loss. Please don't show me how; just point me in the general direction.
 
Physics news on Phys.org
I only have a basic knowledge of trigonometric functions, but without any other indicator of how to approach this I'd put in arbitrary values for the constants a, b, c, d, e, f, g, and h, graph the function, and it seems like you'd be able to derive a method of finding arbitrary periodic sums. Just a thought..
 
Use trig identities for sin2 x and cos2 x.
 
I forgot all about the half-angle identities... Thank you
 

Similar threads

  • · Replies 26 ·
Replies
26
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 9 ·
Replies
9
Views
3K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 31 ·
2
Replies
31
Views
8K
  • · Replies 3 ·
Replies
3
Views
4K
  • · Replies 28 ·
Replies
28
Views
3K
  • · Replies 5 ·
Replies
5
Views
1K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 4 ·
Replies
4
Views
4K