Question

How do you evaluate $\arccos \left( 2 \right)$ ?

Answer 1

Hint : Try to first define the meaning of the above mentioned trigonometric function. Since the angels are mentioned first, try to find where exactly does the values of the trigonometric function lie and then try to calculate its inverse. Sometimes not all the trigonometric functions can be defined.

Complete step-by-step answer :
We have to find the value of $\arccos \left( 2 \right)$ i.e. we have to find the value of the angle of cos say x such that $cos\left( x \right)$ =2
For this first we will have to find the set in which the values of cos generally are.
Clearly we know that $cos\left( x \right)$ has its value in the set [-1, 1] .
From this we can conclude that there is no such angle of cos when it’s value becomes 2.
Hence the question asked to us i.e. $\arccos \left( 2 \right)$ has no value or is insignificant as we have seen above.

Note : As the cos of any number lies between a specified range, so does the sine function. Hence whenever the inverse is asked about the number which does not have the value between the specified range you should never proceed further as the chances are high of the function being undefined.