Algebra 2 Chapter 13

Standard Position

An angle in the coordinate plane is in standard position when the vertex is at the origin and one ray is on the positive x-axis.

Intercepted Arc

An intercepted arc is the portion of the circle with endpoints on the sides of the central angle and remaining points within the interior of the angle.

Central Angle

A central angle of a circle is an angle with a vertex at the center of a circle.

Periodic Function

A periodic function is a function that repeats a pattern of y-values (outputs) at regular intervals.

Cycle

A periodic function is a function that repeats a pattern of y-values (outputs) at regular intervals. One complete pattern is a cycle.

Radian

A radian is the measure of a central angle that intercepts an arc with length equal to the radius of the circle.

Phase Shift

Each horizontal translation of certain periodic functions is a phase shift.

Amplitude

The amplitude is half the difference between the maximum and minimum values of the function.

Cosine Function

The cosine function, y = cos u, matches u with the x-coordinate of the point on the unit circle where the terminal side of angle u intersects the unit circle.

Cosine of 0

The cosine of U (cos u) is the x-coordinate of the point at which the terminal side of the angle intersects the unit circle.

Sine of 0

The cosine of U (cos u) is the x-coordinate of the point at which the terminal side of the angle intersects the unit circle. The sine of U (sin u) is the y-coordinate.

Tangent Function

The graph at the right shows one cycle of the tangent function, y = tan u, for - p 2 6 u 6 p 2 .

Sine Curve

The graph of a sine function is called a sine curve.

Midline

The midline is the horizontal line midway between the maximum and minimum values of a periodic function.

Period

The period of a function is the horizontal length—the distance along the x-axis—of one cycle.

Initial Side

The ray on the x-axis is the initial side of the angle.

Terminal Side

The ray on the x-axis is the initial side of the angle. The other ray is the terminal side of the angle.

Sine Function

The sine function, y = sin u, matches the measure u of an angle in standard position with the y-coordinate of a point on the unit circle.

Unit Circle

The unit circle has a radius of 1 unit and its center at the origin of the coordinate plane.

Tangent of 0

Then the ratio y x is the tangent of U,, denoted tan u.

Coterminal Angles

Two angles in standard position are coterminal angles if they have the same terminal side.