Question

How do you find the value of \[\cos 2\pi ?\]

Answer 1

Hint:
For solving this type of question you should first write what you know. Here we will write some $\sin $and $\cos $formulas. After that, we will relate those formulas to solve our question.

Complete Step by step answer:
This type of question will be solved with many methods.
Some important formulas used to solve this question:
$
  \cos \pi = - 1 \\
  \sin \pi = 0 \\
  \cos (\pi + \theta ) = \cos \pi \cos \theta - \sin \pi \sin \theta \\
  \cos (\pi + \theta ) = - \cos \theta \\
$
Here, question can be written as $\cos 2\pi = \cos (\pi + \pi )$
For solving this question we will use
$\cos (\pi + \theta ) = \cos \pi \cos \theta - \sin \pi \sin \theta $
Here, $\theta = \pi $
After putting the value in formula
$\cos (\pi + \pi ) = \cos \pi \cos \pi - \sin \pi \sin \pi $
$
  \sin \pi = 0 \\
  \cos \pi = - 1 \\
$
After putting the values in formula
$
  \cos 2\pi = ( - 1)( - 1) - 0(0) \\
  \cos 2\pi = 1 \\
$

So, this way you can simply find the value of \[\cos 2\pi \].

Note:
As you can see this type of question is easy to solve when you know the formulas. So for solving this type of question you first find what has been given to you and after that write what you know.