arccos
Represents the inverse cosine (or arccosine) function in trigonometry and mathematical expressions.
Overview
Essential in trigonometry and mathematical analysis for finding angles when given a cosine value, with output ranging from 0 to π radians (0° to 180°).
- Commonly used in geometry and physics calculations involving angular measurements
- Appears frequently in navigation and engineering problems
- Often paired with other inverse trigonometric functions in complex mathematical expressions
- Particularly useful in solving triangles and vector problems where angles need to be determined
Examples
Finding the angle in a right triangle using inverse cosine.
\theta = \arccos\left(\frac{\text{adjacent}}{\text{hypotenuse}}\right)Solving for the angle in a trigonometric equation.
x = \arccos(0.5) = \frac{\pi}{3}Expressing the domain of arccos in an equation.
\arccos(x) \text{ is defined for } -1 \leq x \leq 1