- standard
Prove and apply trigonometric identities
- 9th - 12th Grade
- Michigan State Math Standards
- Functions: Trigonometric Functions
(+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
- standard
Prove and apply trigonometric identities
- 9th - 12th Grade
- Michigan State Math Standards
- Functions: Trigonometric Functions
Prove the Pythagorean identity (sin A)^2 + (cos A)^2 = 1 and use it to find sin A, cos A, or tan A, given sin A, cos A, or tan A, and the quadrant of the angle.
- standard
Model periodic phenomena with trigonometric functions
- 9th - 12th Grade
- Michigan State Math Standards
- Functions: Trigonometric Functions
(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in term…
- standard
Model periodic phenomena with trigonometric functions
- 9th - 12th Grade
- Michigan State Math Standards
- Functions: Trigonometric Functions
(+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.
- standard
Model periodic phenomena with trigonometric functions
- 9th - 12th Grade
- Michigan State Math Standards
- Functions: Trigonometric Functions
Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.*
- standard
Extend the domain of trigonometric functions using the unit circle
- 9th - 12th Grade
- Michigan State Math Standards
- Functions: Trigonometric Functions
(+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
- standard
Extend the domain of trigonometric functions using the unit circle
- 9th - 12th Grade
- Michigan State Math Standards
- Functions: Trigonometric Functions
(+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of…
- standard
Extend the domain of trigonometric functions using the unit circle
- 9th - 12th Grade
- Michigan State Math Standards
- Functions: Trigonometric Functions
Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of ang…
- standard
Extend the domain of trigonometric functions using the unit circle
- 9th - 12th Grade
- Michigan State Math Standards
- Functions: Trigonometric Functions
Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
- standard
Interpret expressions for functions in terms of the situation they model
- 9th - 12th Grade
- Michigan State Math Standards
- Functions: Linear, Quadratic, and Exponential Models
Interpret the parameters in a linear or exponential function in terms of a context.*
- standard
Construct and compare linear, quadratic, and exponential models and solve problems
- 9th - 12th Grade
- Michigan State Math Standards
- Functions: Linear, Quadratic, and Exponential Models
For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm …
- standard
Construct and compare linear, quadratic, and exponential models and solve problems
- 9th - 12th Grade
- Michigan State Math Standards
- Functions: Linear, Quadratic, and Exponential Models
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) …
- standard
Construct and compare linear, quadratic, and exponential models and solve problems
- 9th - 12th Grade
- Michigan State Math Standards
- Functions: Linear, Quadratic, and Exponential Models
Construct and compare linear, quadratic, and exponential models and solve problems. Construct linear and exponential functions, including arithmetic and geomet…
- standard
Construct and compare linear, quadratic, and exponential models and solve problems
- 9th - 12th Grade
- Michigan State Math Standards
- Functions: Linear, Quadratic, and Exponential Models
Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.*