NQ.1.PC.2 Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers). Explain why the rectangular and polar forms of a given complex number represent the same number.
NQ.2.PC Students will perform operations with vectors and use those skills to solve problems
NQ.2.PC.1 Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).
NQ.2.PC.3 Solve problems involving velocity and other quantities that can be represented by vectors.
NQ.2.PC.4 Add and subtract vectors. Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes. Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum. Understand vector subtraction v – w as v + (–w), where –w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order. Perform vector subtraction component-wise.
NQ.2.PC.5 Multiply a vector by a scalar. Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; Perform scalar multiplication component-wise, e.g., as c(vx, v subscript y) = (cvx, cv subscript y). Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).
T.3.PC.2 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 around the unit circle.
T.3.PC.3 Use special right triangles to determine geometrically the exact values of sine, cosine, tangent for π/3, π/4, π/6, and π/2. Use the unit circle to express the values of sine, cosine, and tangent for π–x, π+x, and 2π–x in terms of their exact values for x, where x is any real number.
T.3.PC.4 Develop the Pythagorean identity, sin²(θ) + cos²(θ) = 1. Given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle, use the Pythagorean identity to find the remaining trigonometric functions.
T.4.PC.4 Use inverse functions to: Solve trigonometric equations that arise in modeling context(s); evaluate the solutions of trigonometric equations, with or without technology, and interpret the solutions of trigonometric equations in terms of the context(s).
CS.5.PC.6 Identify, graph, write, and analyze equations of each type of conic section, using properties such as symmetry, intercepts, foci, asymptotes, and eccentricity, and using technology when appropriate.
F.6.PC Students will be able to find the inverse of functions and use composition of functions to prove that two functions are inverses
F.6.PC.1 Write a function that describes a relationship between two quantities. From a context, determine an explicit expression, a recursive process, or steps for calculation. Combine standard function types using arithmetic operations. (e.g., given that f(x) and g(x) are functions developed from a context, find (f + g)(x), (f – g)(x), (fg)(x), (f/g)(x), and any combination thereof, given g(x) ≠ 0.) Compose functions.
F.6.PC.2 Find inverse functions. Solve an equation of the form y = f(x) for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) = 2 x² or (x) = (x + 1)/(x– 1) for x ≠ 1. Verify by composition that one function is the inverse of another. Read values of an inverse function from a graph or a table, given that the function has an inverse. Produce an invertible function from a non-invertible function by restricting the domain.
F.7.PC Students will be able to interpret different types of functions and their key characteristics including polynomial, exponential, logarithmic, power, trigonometric, rational, and other types of functions
F.7.PC.1 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
F.7.PC.3 Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers with coefficients determined for example by Pascal's Triangle.
F.7.PC.4 For a function that models a relationship between two quantities: Interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
F.7.PC.6 Graph functions expressed algebraically and show key features of the graph, with and without technology. Graph linear and quadratic functions and, when applicable, show intercepts, maxima, and minima. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Graph power and polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. Graph exponential and logarithmic functions, showing intercepts and end behavior. Graph trigonometric functions, showing period, midline, and amplitude.
F.7.PC.7 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
F.7.PC.8 Build functions to model real-world applications using algebraic operations on functions and composition, with and without appropriate technology. (e.g., profit functions as well as volume and surface area, optimization subject to constraints).