MA.912.T: Trigonometry

MA.912.T.1: Extend the definitions of the trigonometric functions beyond right triangles using the unit circle, and measure angles in radians as well as degrees. Draw and analyze graphs of trigonometric functions (including finding period, amplitude, and phase shift), and use them to solve word problems. Define and graph inverse trigonometric functions, and determine values of both trigonometric and inverse trigonometric functions.

MA.912.T.1.1: Convert between degree and radian measures.

Cosine Function
Sine Function
Tangent Function

MA.912.T.1.2: Define and determine sine and cosine using the unit circle.

Cosine Function
Sine Function
Translating and Scaling Sine and Cosine Functions

MA.912.T.1.4: Find approximate values of trigonometric and inverse trigonometric functions using appropriate technology.

Sine, Cosine, and Tangent Ratios

MA.912.T.1.5: Make connections between right triangle ratios, trigonometric functions, and circular functions.

Cosine Function
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function

MA.912.T.1.6: Define and graph trigonometric functions using domain, range, intercepts, period, amplitude, phase shift, vertical shift, and asymptotes with and without the use of graphing technology.

Cosine Function
Sine Function
Tangent Function
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions

MA.912.T.1.7: Define and graph inverse trigonometric relations and functions.

Tangent Function

MA.912.T.1.8: Solve real-world problems involving applications of trigonometric functions using graphing technology when appropriate.

Sine, Cosine, and Tangent Ratios

MA.912.T.2: Understand how the trigonometric functions relate to right triangles, and solve word problems involving right and oblique triangles. Understand and apply the laws of sines and cosines. Use trigonometry to find the area of triangles.

MA.912.T.2.1: Define and use the trigonometric ratios (sine, cosine, tangent, cotangent, secant, and cosecant) in terms of angles of right triangles.

Cosine Function
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function

MA.912.T.2.2: Solve real-world problems involving right triangles using technology when appropriate.

Pythagorean Theorem
Pythagorean Theorem with a Geoboard

MA.912.T.3: Know basic trigonometric identities derived from definitions, and use them to prove other identities. Use the sum, difference, double-angle, and half-angle formulas. Solve trigonometric equations and word problems using trigonometry.

MA.912.T.3.2: Use basic trigonometric identities to verify other identities and simplify expressions.

Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine

MA.912.T.3.3: Use the sum and difference, half-angle and double-angle formulas for sine, cosine, and tangent, when formulas are provided.

Sum and Difference Identities for Sine and Cosine

MA.912.T.4: Define, use polar coordinates, and relate them to Cartesian coordinates. Translate equations in terms of Cartesian coordinates into polar coordinates, and graph the resulting equations in the polar coordinate plane. Convert complex numbers from standard to trigonometric form, and vice-versa. Multiply complex numbers in trigonometric form, and use De Moivre?s Theorem.

MA.912.T.4.4: Define the trigonometric form of complex numbers, convert complex numbers to trigonometric form, and multiply complex numbers in trigonometric form.

Points in the Complex Plane