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