Search the California Content Standards

Cluster:
Prove and apply trigonometric identities.

Standard:
Prove the Pythagorean identity sin^2(θ ) + cos^2(θ ) = 1 and use it to find sin(θ ), cos(θ ), or tan(θ ) given sin(θ ), cos(θ ), or tan(θ ) and the quadrant of the angle.

Cluster:
Translate between the geometric description and the equation for a conic section.

Standard:
Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

Cluster:
Translate between the geometric description and the equation for a conic section.

Standard:
Derive the equation of a parabola given a focus and directrix.

Cluster:
Use coordinates to prove simple geometric theorems algebraically.

Standard:
Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2). [Include simple circle theorems.]

Cluster:
Use coordinates to prove simple geometric theorems algebraically.

Standard:
Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

Cluster:
Extend the domain of trigonometric functions using the unit circle.

Standard:
Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

Cluster:
Extend the domain of trigonometric functions using the unit circle.

Standard:
Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

Cluster:
Extend the domain of trigonometric functions using the unit circle.

Standard:
Graph all 6 basic trigonometric functions. CA

Cluster:
Model periodic phenomena with trigonometric functions.

Standard:
Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. *

Cluster:
Prove and apply trigonometric identities.

Standard:
Prove the Pythagorean identity sin^2(θ ) + cos^2(θ ) = 1 and use it to find sin(θ ), cos(θ ), or tan(θ ) given sin(θ ), cos(θ ), or tan(θ ) and the quadrant of the angle.