# How do you find the exact value of #arccos(-1/sqrt(2))#?

##### 3 Answers

#### Explanation:

First, it would be helpful to rationalize

Arccos is asking for the ANGLE with a cosine of the given value.

The range of arccos is between zero and

According to the unit circle, the angle in the second quadrant (between

#### Explanation:

cos x = - 1/(sqrt2) = - sqrt2/2

On the trig unit circle, there are 2 arcs that have the same cos value:

Answers for

Check with calculator:

#### Explanation:

#color(blue)(arccos(-1/(sqrt2))#

First we should understand what the question is about.

It means that, we need to find an angle, when it is inside a cosine function gives

Let's rationalize it

Now let's find out the angle using the unit circle

The angle is