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

  • Thread starter Thread starter solve
  • Start date Start date
AI Thread Summary
The discussion centers on determining when to use ±nπ versus ±2nπ in trigonometric equations. The tangent function has a period of π, while sine and cosine functions have a period of 2π. For the equation tan(4x) = 1, the solution involves ±nπ due to the tangent's periodicity. In contrast, the sine function's periodicity leads to the use of ±2nπ in its solutions. Understanding these periodicities is crucial for correctly applying the appropriate multiples in trigonometric equations.
solve
Messages
94
Reaction score
0

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
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
View full post »

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
View full post »

Similar threads

Finding a domain for a function
Replies
7
Views
2K
How do you know how many solutions there are for z?
Replies
2
Views
1K
So, the real question is:Can (1-cos(npi))=(-1)^(n+1)?
Replies
9
Views
19K
Trigonometric inequality problem.
Replies
5
Views
2K
How do I Graph the Sine Function for y=2-sin(2πx/3)?
Replies
8
Views
2K
How Do You Solve This Trigonometric Limit Problem?
Replies
2
Views
1K
Verify the Trigonometric Identity
Replies
15
Views
2K
1D Particle & Energy w/ F(x): Am I doing this right?
Replies
7
Views
1K
How Do You Calculate the Axes of a Hyperbola Given Its Foci and a Point on It?
Replies
7
Views
2K
Solving trigonometric equation of a sum of unknowns
Replies
7
Views
2K

Hot Threads

Recent Insights

Back
Top