Topic : Trigonometry Course of Study § Semester Course §
1 1.1
Functions & Trigonometry Sets, Functions & Notations – Sets and Venn Diagrams ◦ identify members of sets ◦ basic set operations of union, intersection, and complement ◦ solution sets of algebraic equations expressed in set notation – Functions and their Properties ◦ identify when a relation is a function ◦ find domain and range ◦ use interval notation and identify undefined domains – Graphing Functions ◦ graph linear and quadratic functions ◦ distinguish between odd and even functions ◦ find zeros graphically and algebraically – Inverse of Functions ◦ find the inverse of a linear function ◦ graph the inverse of functions ◦ derermine whether an inverse is a function
1.2
Coordinate Geometry & Trig Ratios – Right Triangles and Pythagorean Theorem ◦ find distance between points ◦ describe linear relations using patterns ◦ describe lines using slope and intercept equations – Functions of Trigonometric Ratios ◦ define ratios of acute angles in the coordinate plane ◦ describe domain and range of sine/cosine functions ◦ angles in a triangle vs. angles of rotation ◦ identify reference and coterminal angles ◦ unit circle – Tangent and Slope ◦ use the slope of a line to find tangent ◦ determine domain / range of tangent function
Trigonometry
1.3
Notes/Lessons
Mr. Farzad : JLHS
Values of Trigonometric Functions – Special Right Triangles ◦ find values of trig functions for special angles ◦ use special values to solve for sides of right triangles ◦ use symmetry and reference angles to determine values – Inverse of Trigonometric Functions ◦ describe domain and range ◦ find inverse values and explain its meaning ◦ using inverse in triangles – Principal Values ◦ determine possible inverse values ◦ solve equations with inverse values – Graphing Intro ◦ use domain and range to graph sine and cosine ◦ use special angle points ◦ graph inverse functions of sine and cosine
2 2.1
Applications of Trigonometric Functions to Triangles Solving Triangles – Right Triangles ◦ use trig functions and inverse to solve applied problems ◦ finding areas of triangles – Non-Right Triangles part I ◦ applying law of sines where possible ◦ applications to surveying and navigation ◦ determining when law of sines will not work – Non-Right Triangles part II ◦ applying law of cosines where possible ◦ using law of sines to complete solutions ◦ further applications – Areas of Triangles Revisited ◦ use law of sines or cosines ◦ use Heron’s formula – Exploring Law of Tangents ◦ show relation to law of cosines / sines ◦ use to solve triangles
2
Trigonometry
2.2
Notes/Lessons
Arcs and Circles – Central Angles and Arcs ◦ finding arc length ◦ finding sector area ◦ finding area of segment – Radians ◦ defining radians in terms of circumference ◦ replacing degrees with radians in a circle ◦ using radians for arc length and sector area – Applications to Angular Velocity ◦ linear vs. angular velocity ◦ applications to orbitals
3 3.1
Extending Unit Circle & Exploring Identities Circular Functions – Period Nature of Trig Functions ◦ identify periods of functions using domain and range ◦ affects of period change on graphs of sine and cosine – Related Periodic Functions ◦ identify reciprocal functions, their domain and range ◦ identify cofunctions, their domain and range – Geometry of related functions ◦ using right triangles to find reciprocal function values ◦ using right triangles to find cofunction values ◦ exploring symmetry on a circle
3.2
Identities – Pythagorean Identities ◦ define an identity ◦ difference between identity and function ◦ use counterexamples to discover non-identities – Verifying Identities ◦ ◦ ◦ ◦
algebraic verification using graphing/numerical tools to verify simplifying identities rewriting identites
3
Mr. Farzad : JLHS
Trigonometry
Notes/Lessons
Mr. Farzad : JLHS
– Sum & Difference ◦ ◦ ◦ ◦
show how to find sum and difference identities of cosine explore sine and tangent identities apply identities to special angles find and verify symmetry identities
– Double and Half Angle ◦ show double angle identities for trig functions ◦ apply identities to solve problems
4 4.1
Amplitude, Frequency & Graphing Graph Properties of Periodic Functions – Period and Frequency ◦ understand relation between period and frequency ◦ find the period and frequency of sine / cosine function ◦ noting the difference between tangent vs. sine ◦ determining phase shifts in graphs ◦ determining phase shifts from equations – Amplitude ◦ ◦ ◦ ◦
define and describe amplitude amplitude and range values of functions periodic functions without amplitude application problems with amplitude
– More Graphs of Trig Functions ◦ graphing cosecant and secant ◦ graphing inverse sine and inverse cosine ◦ undersanding the need for Principal Values to make inverse sine and cosine functions 4.2
Graphing Equations – Transformations of Trig Functions ◦ understanding phase shift and horizontal displacement ◦ accounting for amplitude and vertical shift of midline ◦ affects of change in period – Graphing Techniques ◦ dealing with transformations algebraically ◦ using geometry and symmetry to transform graphs ◦ more graphing practice
4
Trigonometry
Notes/Lessons
– Tangent and Cotangent ◦ using graphing techniques with tan and cot ◦ graphs of inverse trig functions ◦ applications and interpreting graphs
5 5.1
Further Applications of Trigonometry Vectors – Unit Vectors and Addition ◦ define and find vector magnitude and direction ◦ find verical and horizontal components ◦ use multiple ways to compute vector sum ◦ find equivalent vectors with given direction and magnitude – Dot Product and Linear Systems ◦ find inner product of two vectors ◦ find angle between two vectors ◦ use vectors to find area ◦ linear systems using dot product – Cross Product and Matrices ◦ compute cross product ◦ interpret cross product in physical terms ◦ solve application problems
5.2
Complex Numbers – Basic Operations ◦ find sum and difference ◦ find products and quotients ◦ graph complex numbers ◦ find the modulus ◦ explore complex conjugates with quadratics – Euler’s Formula ◦ convert between a + ib and keiθ ◦ use DeMoivre’s Theorem ◦ find roots of complex numbers
5.3
Polar Coordinates – – – –
Graphing Polar Equations Linear and Polar Conversions Vector Applications Numerical Methods 5
