# How do you find the exact value of # arccos(cos (7pi)/6)#?

##### 2 Answers

Find the exact value of

Ans:

#### Explanation:

#### Explanation:

Typically, the arccosine function works as such:

#arccos(cos(x))=x#

So here, you would think that:

#arccos(cos((7pi)/6))=(7pi)/6#

However, this is ** not true**!

The range of the arccosine function, that is, the values that the arccosine function can spit out, is restricted from

Since

The best way to think about this is that

Since cosine is negative in the third quadrant, we will need an angle with a reference angle of

Since to fit in that range the angle must be in the first or second quadrant, and since cosine is negative, we want the angle from the second quadrant.

The angle with a reference angle of

Thus:

#arccos(cos((7pi)/6))=(5pi)/6#