Content Standards

T.2.0: Students know the definition of sine and cosine as y- and x-coordinates of points on the unit circle and are familiar with the graphs of the sine and cosine functions.

Cosine Function

Sine Function

Sine and Cosine Ratios - Activity A

Sine, Cosine and Tangent

Tangent Function

Unit Circle

T.3.1: Students prove that this identity is equivalent to the Pythagorean theorem (i.e., students can prove this identity by using the Pythagorean theorem and, conversely, they can prove the Pythagorean theorem as a consequence of this identity).

Simplifying Trigonometric Expressions

T.3.2: Students prove other trigonometric identities and simplify others by using the identity cos²(x) + sin²(x) = 1. For example, students use this identity to prove that sec²(x) = tan²(x) + 1.

Simplifying Trigonometric Expressions

T.4.0: Students graph functions of the form f(t) = A sin (Bt + C) or f(t) = A cos (Bt + C) and interpret A, B, and C in terms of amplitude, frequency, period, and phase shift.

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions - Activity A

T.5.0: Students know the definitions of the tangent and cotangent functions and can graph them.

Tangent Function

Tangent Ratio

T.7.0: Students know that the tangent of the angle that a line makes with the x-axis is equal to the slope of the line.

Slope - Activity B

Tangent Function

Tangent Ratio

T.9.0: Students compute, by hand, the values of the trigonometric functions and the inverse trigonometric functions at various standard points.

Cosine Function

Sine Function

Tangent Function

T.10.0: Students demonstrate an understanding of the addition formulas for sines and cosines and their proofs and can use those formulas to prove and/or simplify other trigonometric identities.

Sum and Difference Identities for Sine and Cosine

T.11.0: Students demonstrate an understanding of half-angle and double-angle formulas for sines and cosines and can use those formulas to prove and/or simplify other trigonometric identities.

Sum and Difference Identities for Sine and Cosine

T.12.0: Students use trigonometry to determine unknown sides or angles in right triangles.

Sine and Cosine Ratios - Activity A

Sine, Cosine and Tangent

T.15.0: Students are familiar with polar coordinates. In particular, they can determine polar coordinates of a point given in rectangular coordinates and vice versa.

Complex Numbers in Polar Form

Points in Polar Coordinates

T.16.0: Students represent equations given in rectangular coordinates in terms of polar coordinates.

Complex Numbers in Polar Form

Points in Polar Coordinates

T.17.0: Students are familiar with complex numbers. They can represent a complex number in polar form and know how to multiply complex numbers in their polar form.

T.18.0: Students know DeMoivre's theorem and can give nth roots of a complex number given in polar form.

Correlation last revised: 9/11/2014

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.