+-2npi OR +-npi How do you know which one to attach?

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Homework Help Overview

The discussion revolves around determining the appropriate periodicity to apply when solving trigonometric equations, specifically in the context of the tangent and sine functions. The original poster presents two equations involving tangent and sine, questioning the use of ±nπ versus ±2nπ in their solutions.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to understand the reasoning behind attaching ±nπ or ±2nπ to their solutions, suspecting it relates to the periods of the trigonometric functions. Some participants engage by asking about the periods of the tangent, sine, and cosine functions.

Discussion Status

Participants have confirmed the periods of the tangent, sine, and cosine functions, indicating a productive exchange of information. However, the original poster's specific question about the application of these periods remains open for further exploration.

Contextual Notes

The original poster expresses uncertainty regarding their understanding of the periodic properties of trigonometric functions, which may influence their application in solving the equations presented.

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Homework Statement



a. tan4x=1

If tanTheta=1, then Theta=pi/4+-npi radians.

4x=pi/4+-npi

x=pi/16+-npi/4

b. sin(x+2pi)+sin(x-2pi)=1/2

sinxcos2pi+cosxsin2pi+sinxcos2pi-sin2picosx=1/2

2sinxcos2pi=1/2

sinxcos2pi=1/4

sinx=1/4

arcsin(1/4)=0.2526+-2npi



Homework Equations


The Attempt at a Solution



So how do you know which one to attach +-npi or +-2npi? I have a slight suspicion that it might be due to periods of trig functions, but I don't trust myself when it comes to math.

Thanks.
 
Physics news on Phys.org
What is the period of the tangent function, and what is the period of the sine and the cosine functions?

ehild
 
ehild said:
What is the period of the tangent function, and what is the period of the sine and the cosine functions?

ehild

The tangent function repeats itself every pi and sine cosine functions repeat every 2pi?
 
Yes, correct.

ehild
 
Thank You, Ehild.
 
solve said:
Thank You, Ehild.

You are welcome.

ehild
 

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