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

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In summary, when solving for x in equations involving trigonometric functions, it is important to take into account their periods. For the equation tan4x=1, the solution is x=pi/16+-npi/4. For the equation sin(x+2pi)+sin(x-2pi)=1/2, the solution is x=0.2526+-2npi. This is because the period of the tangent function is pi, while the period of the sine and cosine functions is 2pi.
  • #1
solve
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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.
 
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  • #2
What is the period of the tangent function, and what is the period of the sine and the cosine functions?

ehild
 
  • #3
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?
 
  • #4
Yes, correct.

ehild
 
  • #5
Thank You, Ehild.
 
  • #6
solve said:
Thank You, Ehild.

You are welcome.

ehild
 

1. What is +-2npi and +-npi?

+-2npi and +-npi are both mathematical expressions that represent a range of values on the unit circle. They are commonly used in trigonometry and other branches of mathematics.

2. How do they differ from each other?

+-2npi represents a larger range of values than +-npi. Specifically, +-2npi represents values from -2pi to 2pi, while +-npi represents values from -pi to pi.

3. How do you know which one to attach to a given value?

This depends on the context and what the value represents. If the value is an angle in radians, it is typically attached to either +-2npi or +-npi depending on the desired range. If the value represents a periodic function, such as sine or cosine, it is usually attached to +-2npi to show the full period.

4. Are there any other common uses for these expressions?

Yes, +-2npi and +-npi can also be used to represent the number of rotations or revolutions. For example, if an object completes 3 rotations, it is equivalent to 6pi or 2npi.

5. Can these expressions be simplified?

Yes, both +-2npi and +-npi can be simplified to just npi, where n is any integer. This is because the values on the unit circle repeat every 2pi, making the larger expressions unnecessary in some cases.

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