Write an expression for x which describes all values such that cos(x) = 1?

Question

is x = 2pi * n correct?

Or is it x = 2pi + n? and WHY

Answer 1

If the solution is 2pi, then another solution is 4 pi.... 6pi.. 8pi... all these terminate in the same place on the unit circle..

All of these are multiples of 2pi.. so your first answer was correct (if n is an integer)

Answer 2

Think of all the values for which this works: "any angle at 0 or coterminal with 0," right? So this is 0 + any multiple of 2pi, which is 0 + 2pi*n where n is an integer. You don't need the 0 in this case, so 2pi*n is the answer.

Answer 3

The answer is 2pi*n - assuming n is a member of the natural numbers!

The reason for this is that cos(X) = 1 ONLY once every cycle. Where one whole cylce (i.e. 360 degrees is equivalent to 2Pi, and it follows that 1/2 a cycle= Pi...thus pi= 180 degrees) is represented by 2Pi. Thus the values of n can be 0,1,2,3,4,..., up to infinity. And n represents the number of complete cycles. Therefore, this works for every value of n!
Hope this helps

Answer 4

x=2pi*n when n is any integer including 0. if it were plus n then that would mean that cos(5.1415...)=1, which is obviously wrong. cos(x) only =1 at the angle of 0, which is the same as any multiple of 2pi.

Answer 5

It's 2 pi*n, because cos 0 = 1

Every time you do a 2pi, you come back to 0

Answer 6

x = 2pi * n cause x = 2pi + n is not a cyclic function

Answer 7

the respond is 0 2 (-a million) - 3(-a million) 2 -2( 3 ) - (-3)2 -6 minus -6 = 0 The adverse 6's cancel one yet another out. XY = the quantity you may multiply via. every time there's a 2x3 - the x is often mulitplied until seperated via a distinctive image

Answer 8

2Pi*n

Ignore my unedited answer, this is correct.

Look at the graph for intuition: the solutions are at x = 0, 2Pi, 4Pi, 6Pi, etc., or 2Pi*n

Answer 9

2 pi n is correct becuase it is periodic ,period 2pi

Answer 10

cos(x) = 1
cos(x) = cos(2* pi*n)=1
for n=0,1,2,...

x=2*pi* n
is the answer.