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.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, 2018HSF.TF.A1
Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
October 1, 2018HSF.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, 2018HSF.TF.A3
(+) 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 sine, cosine, and tangent for x, π + x, and 2π – x in terms of their values for x, where x is any real number.
October 1, 2018HSF.TF.A4
(+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
October 1, 2018