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.

Answer

\( \frac{\pi}{2} \)
Answer for screen readers

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} )

More Information

The arccosine function is used to find the angle in a right-angled triangle when the cosine value is known. It is particularly useful in trigonometry, physics, and engineering.

Tips

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.

Thank you for voting!
Use Quizgecko on...
Browser
Browser