Arccosine

Definition

Arccosine, denoted as $\arccos(x)$ or $\cos^{-1}(x)$, is the inverse function of the cosine function. It returns the angle whose cosine is a given number within the interval [0, π].

5 Must Know Facts For Your Next Test

1. The domain of the arccosine function is [-1, 1] and the range is [0, π].
2. $\arccos(1) = 0$ and $\arccos(-1) = \pi$.
3. For any $x$ in [-1, 1], $\cos(\arccos(x)) = x$.
4. Arccosine is used to solve for an angle in a right triangle when you know the adjacent side and hypotenuse.
5. The derivative of $y = \arccos(x)$ with respect to $x$ is $\frac{-1}{\sqrt{1-x^2}}$.

Review Questions

• What is the range of the arccosine function?
• Calculate $\arccos(0.5)$.
• What is the derivative of $y = \arccos(x)$?

Related terms

Cosine: A fundamental trigonometric function that relates the angle to the ratio of the adjacent side over hypotenuse in a right triangle.

Inverse Trigonometric Functions: Functions that reverse trigonometric functions such as sine, cosine, and tangent to obtain angles from ratios.

$\arcsin(x)$: $\text{Arcsine}$: The inverse of sine function returns an angle whose sine value equals a given number, with domain [-1, 1] and range [-π/2, π/2].