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sara_87
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Homework Statement
what is cos(2n*pi)
Homework Equations
The Attempt at a Solution
I understand that cos(npi)=(-1)^n
so is cos(2n*pi)=2(-1)^n ??
No. Look at posts 4 and 7.sara_87 said:oh right,
so =(-1)^(n+1)
is that right?
HallsofIvy said:Do you know what cos(0) is? Do you know that cosine is periodic with period 2 pi?
sara_87 said:yep cos0=1
yep, cos is periodic with period 2pi
HallsofIvy said:So cos(2n pi)= cos(0+ n(2pi))= ?
Okay, what does "periodic" mean?sara_87 said:oh right,
so =(-1)^(n+1)
is that right?
Would it be easier if it were written n*(2pi) rather than 2n*pi? This is about multiples of 2pi!sara_87 said:I understand that periodic means that cosine function repeats after multiples of 2 pi. but how would that have anything to do with writing cos(2n*pi) ?
cos (npi)=(-1)^n because as long as n is an integer, the value will alternate from -1 and 1 (clearly form the graph)
Cos(2n*pi) refers to the cosine function with an argument of 2n times pi, where n is any integer. This expression represents the cosine of an angle that is a multiple of 360 degrees, which is equivalent to one full rotation on a unit circle.
When graphed on a unit circle, the cosine function with an argument of 2n times pi will produce a wave-like pattern that repeats every 360 degrees or 2pi radians. This is because the cosine function represents the x-coordinate of a point on the unit circle, and as the angle increases by a multiple of 360 degrees, the x-coordinate will return to its original value.
The range of values for cos(2n*pi) is between -1 and 1. This is because the cosine function can never produce a value outside of this range, as it represents the ratio of the adjacent side to the hypotenuse in a right triangle.
Cos(2n*pi) can be used in a variety of real-world applications, such as in physics, engineering, and navigation. It can be used to calculate the amplitude of a wave, the position of an object in circular motion, or the phase difference between two waves.
Yes, cos(2n*pi) can have a value of 0 when the argument is a multiple of 90 degrees or pi/2 radians. This occurs at angles of 0, 90, 180, 270 degrees, and so on, where the cosine function will output a value of 0. This can also be seen on the unit circle, where the x-coordinate of these angles is 0.