Inverse trigonometric functions

Definition

Inverse trigonometric functions are the inverse operations of the basic trigonometric functions (sine, cosine, and tangent). They are used to find angles when given a ratio of sides in right triangles.

5 Must Know Facts For Your Next Test

1. The principal values of the inverse sine function, $\text{sin}^{-1}(x)$ or $\arcsin(x)$, range from $-\frac{\pi}{2}$ to $\frac{\pi}{2}$.
2. The principal values of the inverse cosine function, $\text{cos}^{-1}(x)$ or $\arccos(x)$, range from $0$ to $\pi$.
3. The principal values of the inverse tangent function, $\text{tan}^{-1}(x)$ or $\arctan(x)$, range from $-\frac{\pi}{2}$ to $\frac{\pi}{2}$.
4. Inverse trigonometric functions are often used to solve equations involving trigonometric expressions by isolating the angle variable.
5. $y = \text{sin}^{-1}(x), \text{cos}^{-1}(x), \text{and tan}^{-1}(x)$ can be interpreted as finding an angle whose sine, cosine, and tangent is x respectively.

Review Questions

• What is the range of the principal values for the inverse sine function?
• How would you express an angle whose cosine value is known using an inverse trigonometric function?
• What are common applications where you might use inverse trigonometric functions?

Related terms

Sine Function: A fundamental trigonometric function that relates an angle in a right triangle to the ratio of the opposite side over the hypotenuse.

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

Tangent Function: A fundamental trigonometric function that relates an angle in a right triangle to the ratio of the opposite side over the adjacent side.