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.