# High School: Functions

##### HSF.TF.C9

(+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

October 1, 2018##### HSF.TF.C8

Prove the Pythagorean identity sin2(θ) + cos2(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.

October 1, 2018##### HSF.LE.A4

For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

October 1, 2018##### HSF.LE.A1

Distinguish between situations that can be modeled with linear functions and with exponential functions.

October 1, 2018##### HSF.LE.A1a

Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

October 1, 2018##### HSF.LE.A1b

Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

October 1, 2018##### HSF.LE.A1c

Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

October 1, 2018##### HSF.LE.A2

Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

October 1, 2018##### HSF.LE.A3

Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

October 1, 2018##### HSF.LE.B5

Interpret the parameters in a linear or exponential function in terms of a context.

October 1, 2018##### HSF.TF.A1

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

October 1, 2018##### HSF.TF.A2

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.

October 1, 2018