how do you solve cos (x)=1?

Question

i need help!

Answer 1

x = 0 ° , x = 360 °

Answer 2

You just have to KNOW some standard results; among those are things like

cos (0) = 1.

The principle root is x = 0; or, in general, x = 2nπ radians for any integer n, +ve or -ve.

It's clear geometrically if you think of the implication of the mnemonic definition, "cos θ = A/H," where θ is the relevant angle, A is the "adjacent side" and H is the hypoteneuse of the right-angled triangle containing the angle θ. Clearly cos θ is generally < 1. However, as θ is made smaller, cos θ will increase. It can only become equal to 1 in the very limit when x = 0.

You could also deduce this from the expansion for cos x:

cos x = 1 - x^2/2! + x^4/4! - x^6/6! + ... .

While the solution to this for non-zero x (or even whether there IS one) is definitely NOT obvious, it is clear that for x = 0 you have your solution.

However, these solutions don't help you learn that there is a general solution x = 2nπ radians unless you think of extending the geometrical interpretation outside the domain of the usual four quadrants.

Live long and prosper.

Answer 3

cos x=1 x =cos-1(1)
x=0

Answer 4

You could take the inverse cosine of both sides, but this still demands you know what angle gives a cosine of 1. Learn the sine and cosine values for the common angles like 0, 30, 60, 45 and 90, then how to derive the other angles from those.

The answer by the way is x = 0.

Answer 5

what angle has a cosine of 1 is the question.
cosine is the x value of the points on the unit circle.
You'll notice that x=1 at 0 degrees. So the cosine of 0, 360, 720, etc is 1.

Answer 6

The best way to solve this equation is to say, "at what point x along the cosine graph is the y equal to 1?"

Look at the cosine graph and I'm sure by that graph you would see that x would equal: 0 or it could equal 2pi.

Here's a link to check it out: http://blue.utb.edu/bentonsc/math1412/resources_files/image030.jpg

I hope that helps you out! Please let me know if you have any other questions!

Sincerely,

Andrew

Answer 7

they easiest (but not best) way to solve this is using a calculator, preferrably a graphing calculator. Type [cos] and [x] and [=] , [1]. Answer is 0