Math127 Inverse Trig Functions

Inverse Function

A function that reverses the effect of the original function; for example, sine inverse returns the angle whose sine is a given value.

Domain

The set of all possible input values (x-values) for a function.

Range

The set of all possible output values (y-values) for a function.

Sine Inverse (sin⁻¹)

The inverse function of sine, used to find the angle that corresponds to a given sine value.

Cosine Inverse (cos⁻¹)

The inverse function of cosine, used to find the angle that corresponds to a given cosine value.

Tangent Inverse (tan⁻¹)

The inverse function of tangent, used to find the angle that corresponds to a given tangent value.

Reference Angle

The acute angle formed by the terminal side of a given angle and the x-axis.

Quadrants

The four sections of the Cartesian plane, labeled as I, II, III, and IV, based on the sign of the coordinates, where each quadrant has specific trigonometric sign rules.

π/6

An angle of 30 degrees, often associated with sine being 1/2 and cosine being √3/2.

π/3

An angle of 60 degrees, often associated with sine being √3/2 and cosine being 1/2.

Boundary Values

Values at the edge of the domain that determine where a function can be evaluated.

Rationalize

To eliminate the square root in the denominator of a fraction.

Sine (sin)

A trigonometric function that relates the angle in a right triangle to the ratio of the length of the opposite side to the hypotenuse.

Cosine (cos)

A trigonometric function that relates the angle in a right triangle to the ratio of the length of the adjacent side to the hypotenuse.

Tangent (tan)

A trigonometric function that relates the angle in a right triangle to the ratio of the length of the opposite side to the adjacent side.

Exact Value

Specific values that result from trigonometric functions evaluated at known angles, such as 30°, 45°, and 60°.

Calculator Error

A message indicating that a value is outside the valid input range for a function; for example, sin⁻¹ of a number greater than 1 or less than -1.

Negative Angle

An angle measured in the clockwise direction from the positive x-axis, typically indicating a reflection across the x-axis.

Sine Graph

A graphical representation of the sine function, showing periodic behavior and the values of sine for various angles.

Trigonometric Equations

Mathematical statements involving trigonometric functions and variables that need to be solved for the variable.

Inverse Function Cancellation

The property where applying a function and its inverse in succession returns the original input.

Angle Measurement

The process of quantifying the size of an angle, typically in degrees or radians.

Identity

An equation that is true for all values of the variable within a given domain.