# arccos 0

#### Understand the Problem

The question is asking for the value of the arccosine function at 0. This involves understanding the properties of the arccos function and what angles correspond to a cosine value of 0.

$$\frac{\pi}{2}$$

The final answer is ( \frac{\pi}{2} )

#### Steps to Solve

1. Identify the meaning of arccos

Arccosine (or inverse cosine) of a number is the angle whose cosine is that number. So we're looking for the angle ( \theta ) such that

$$\cos(\theta) = 0$$

1. Determine the range of arccos function

The range of the arccos function is from 0 to ( \pi ) (or from 0 to 180 degrees). So we only consider angles in this range.

1. Find the angle whose cosine is 0 in the given range

The cosine of 0 is equal to 0 at ( \theta = \frac{\pi}{2} ) (or 90 degrees). This angle lies within the range of the arccos function.

Therefore:

$$\text{arccos}(0) = \frac{\pi}{2}$$

The final answer is ( \frac{\pi}{2} )

A common mistake is incorrectly identifying the range of the arccos function. Make sure to only consider angles between 0 and $\pi$ for the arccos function.