High School: Functions
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, 2018HSF.TF.C9
(+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
October 1, 2018HSF.TF.B6
(+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.
October 1, 2018HSF.TF.B7
(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.*
October 1, 2018HSF.LE.A1
Distinguish between situations that can be modeled with linear functions and with exponential functions.
October 1, 2018HSF.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, 2018HSF.LE.A1b
Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
October 1, 2018HSF.LE.A1c
Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
October 1, 2018HSF.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, 2018HSF.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, 2018HSF.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, 2018HSF.LE.B5
Interpret the parameters in a linear or exponential function in terms of a context.
October 1, 2018