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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.

θ=arccos(adjacenthypotenuse)\theta = \arccos\left(\frac{\text{adjacent}}{\text{hypotenuse}}\right)
\theta = \arccos\left(\frac{\text{adjacent}}{\text{hypotenuse}}\right)

Solving for the angle in a trigonometric equation.

x=arccos(0.5)=π3x = \arccos(0.5) = \frac{\pi}{3}
x = \arccos(0.5) = \frac{\pi}{3}

Expressing the domain of arccos in an equation.

arccos(x) is defined for 1x1\arccos(x) \text{ is defined for } -1 \leq x \leq 1
\arccos(x) \text{ is defined for } -1 \leq x \leq 1