Kinematics is all about motion. Motion is a change in position relative to a frame of reference
scalar vs vector distance vs displacement speed vs velocity frame of reference acceleration
Vectors can be manipulated in two ways, by trigonometry or on a Cartesian coordinate system
$$d = v_it + \frac{1}{2}at^2$$ $$v_f^2 = v_i^2 + 2ad$$ $$v_f = v_i + at$$ $$d = \frac{v_i + v_f}{2}t$$
Connecting Graphs and Equations of Quadratic Relations
Connecting Graphs and Equations fo Exponenetial Realtions
SOlving Problems Incolving Exponenetial Relations
Solving Problems Involving Compound INtersets
Comparing Financial Services
Owning and Operating a Vehicle
Representing 2D Shapes and 3D Ficulres
Applying the Sine and Cosine Laws in Acute Triangles
Working with 1-Variable Data
Applying Probability
The purpose of this project is to produce a report on the sunspot cycle and how you developed a mathematical model of it. The report should be 2-3 pages long and include
2.5 determine, through investigation using technology, the roles of the parameters a, k, d, and c in functions of the form y =af (k(x – d)) + c, where f(x) =sinx or f(x) =cosx with angles expressed in degrees, and describe these roles in terms of transformations on the graphs of f(x) =sinx and f(x) =cosx
art supplies, computer access
2.4 sketch the graphs of f(x) =sinx and f(x) =cosx for angle measures expressed in degrees, and determine and describe their key properties
2.6 determine the amplitude, period, phase shift, domain, and range of sinusoidal functions whose equations are given in the form f(x) = asin(k(x – d)) + c or f(x) = acos(k(x – d)) + c
2.7 sketch graphs of y = af (k(x – d)) + c by applying one or more transformations to the graphs of f(x) =sinx and f(x) =cosx, and state the domain and range of the transformed functions
2.5 determine, through investigation using technology, the roles of the parameters a, k, d, and c in functions of the form y =af (k(x – d)) + c, where f(x) =sinx or f(x) =cosx with angles expressed in degrees, and describe these roles in terms of transformations on the graphs of f(x) =sinx and f(x) =cosx
2.4 sketch the graphs of f(x) =sinx and f(x) =cosx for angle measures expressed in degrees, and determine and describe their key properties
Internet, graph paper or a printer, radian to degrees cheat-sheet
2.1 describe key properties of periodic functions arising from real-world applications, given a numeric or graphical representation
2.2 predict, by extrapolating, the future behavior of a relationship modeled using a numeric or graphical representation of a periodic function
Computer Lab
amplitude, period, sunspot, solar cycle
None beyond previous lessons in unit.
2.3 make connections between the sine ratio and the sine function and between the cosine ratio and the cosine function by graphing the relationship between angles from 0º to 360º and the corresponding sine ratios or cosine ratios, defining this relationship as the function f(x) =sinx or f(x) =cosx, and explaining why the relationship is a function
2.4 sketch the graphs of f(x) =sinx and f(x) =cosx for angle measures expressed in degrees, and determine and describe their key properties
Spaghetti, yarn, paper, glue.
The universe if full of phenomenon that are cyclical or follow a repeating pattern. Many of these can be modeled using sinusoidal functions.
2.1 describe key properties of periodic functions arising from real-world applications given a numeric or graphical representation
2.2 predict, by extrapolating, the future behavior of a relationship modeled using a numeric or graphical representation of a periodic function
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