Question

When \[cosx = 1\] what does \[x\] equal ?

Answer 1

Hint: In this given question, we need to find the value of \[x\]. Given that \[cosx=1\] . The basic trigonometric functions are sine , cosine and tangent. Cosine is nothing but a ratio of the adjacent side of a right angle to the hypotenuse of the right angle . Here we need to find the value of \[x\] when \[cosx=1\] . With the help of the Trigonometric functions , we can find the value of \[x\].

Complete step by step solution:
Given, \[cosx = 1\]
We need to find the value of \[x\].
By taking inverse of cosine on both sides of the given expression,
We get,
\[cos^{- 1}(cosx)\ = \cos^{- 1}(1)\]
On simplifying,
We get,
\[x = cos^{- 1}(1)\]
\[x\] can be any integer multiple of \[2\pi\] including \[0\].
⇒ \[cos(2n\pi)\ = 1\] for any integer \[n\] including \[0\] . \[(n\ \in \ Z)\]
The period of cosine function is \[2\pi\] .
That is \[x = 2n\pi\] where \[n \in Z\]
By substituting \[n = 0\] ,
We get, \[x = 0\]
By substituting \[n = 1\] ,
We get, \[x = 2(1)(180)\]
By multiplying,
We get, \[x = 360\]
Hence the value of \[x = 0^{o},\ 360^{o}\], and so on.
Therefore \[x = 2n\pi\] where \[n \in Z\]
Final answer :
When \[cosx = 1\] , the value of \[x = 2n\pi\] where \[n \in Z\]

Note: The concept used in this problem is trigonometric identities and ratios. Trigonometric identities are nothing but they involve trigonometric functions including variables and constants. The common technique used in this problem is the use of trigonometric functions . Trigonometric functions are also known as circular functions or geometrical functions. The inverse of the cosine function is nothing but it is a cosine function raised to the power of \[(-1)\] .