1 Functions & Trigonometry

Transcription

1 Semester : IISME - ETP Topic : Trigonometry Course of Study Semester Course Mr. Farzad : JLHS 1 Functions & Trigonometry 1.1 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

2 1.3 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 Applications of Trigonometric Functions to Triangles 2.1 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

3 2.2 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 Extending Unit Circle & Exploring Identities 3.1 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 3.2 Identities using right triangles to find reciprocal function values using right triangles to find cofunction values exploring symmetry on a circle 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

4 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 Amplitude, Frequency & Graphing 4.1 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

5 Tangent and Cotangent using graphing techniques with tan and cot graphs of inverse trig functions applications and interpreting graphs 5 Further Applications of Trigonometry 5.1 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 ke iθ 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