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Transformations of Sine and Cosine Functions MHF4UI Tuesday November 13 th, 2012
Relating Trig Functions to Angles in Standard Position
The General Form of Sinusoidal Functions
The General Form of Sinusoidal Functions (Continued)
Applying Transformations Example 1
Applying Transformations Example 2
Mapping Notation for Sinusoidal Functions
Graphing Sine and Cosine Functions When sketching a sine or cosine function, you must: Label all 5 key points (After you have applied the mapping notation) Show the general shape of the graph.
Graphing Sine and Cosine Functions Example 1
Graphing Sine and Cosine Functions Example 2
Graphing Sine and Cosine Functions Example 3
Homework Questions: Complete the Transformations Worksheet Handout
Graphing Primary and Reciprocal Trig Functions MHF4UI Monday November 12 th, 2012.
Trig Functions Review (Including Trig Quiz Solutions) MHF4UI Friday November 16 th, 2012.
WARM-UP: USE YOUR GRAPHING CALCULATOR TO GRAPH THE FOLLOWING FUNCTIONS Look for endpoints for the graph Describe the direction What is the shape of the.
The sine rule When the triangles are not right-angled, we use the sine or cosine rule. Labelling triangle Angles are represented by upper cases and sides.
Aim: What is the transformation of trig functions? Do Now: HW: Handout Graph: y = 2 sin x and y = 2 sin x + 1, 0 ≤ x ≤ 2π on the same set of axes.
Graphs of the Sine and Cosine Functions Section 6.
Trig – Section 4 Graphing Sine and Cosine Objectives: To graph sine and cosine curves To find amplitude, period and phase shifts.
Module 6.4 Graphing Sine and Cosine Functions with Different Amplitudes and Periods.
Shapes and Angle Rules 80 + ? = = 180.
CHAPTER 5 LESSON 4 The Law of Sines VOCABULARY None.
Chapter 4 Trigonometric Functions The Unit Circle Objectives: Evaluate trigonometric functions using the unit circle. Use domain and period.
Periodic Functions A periodic function is a function for which there is a repeating pattern of y-values over equal intervals of x. Each complete pattern.
Precalculus 4.7 Inverse Trigonometric Functions 1 Bellwork Use your unit circle to find the possible values of Keep the unit circle handy for reference.
Pg. 407/423 Homework Pg. 407#33 Pg. 423 #16 – 18 all #19 Ѳ = kπ#21t = kπ, kπ #23 x = π/2 + 2kπ#25x = π/6 + 2kπ, 5π/6 + 2kπ #27 x = ±1.05.
Section Inverse Sine and Cosine. Lesson Objective: Students will: Graph the relations for inverse sine and cosine. Restrict the range for to make.
Today you will use shifts and vertical stretches to graph and find the equations of sinusoidal functions. You will also learn the 5-point method for sketching.
5.7 Inverse Trig Functions. Does the sine function have an inverse?
3.5 – Derivative of Trigonometric Functions Derivative Notation REVIEW: Function Notation.
Chapter 4 Trigonometric Functions Inverse Trigonometric Functions Objectives: Evaluate inverse sine functions. Evaluate other inverse trigonometric.
Notes Over 14.1 Graph Sine, Cosine, and Tangent Functions.
Do Now: Graph the equation: X 2 + y 2 = 1 Draw and label the special right triangles What happens when the hypotenuse of each triangle equals 1?
20 Days. Three days Graphing Sine and Cosine WS.
Sine Law Homework Questions??? Pg. 25 # 3, 5, 7, 9.
Sullivan Precalculus: Section 5.4 Graphing the Sine and Cosine Functions Objectives of this Section Graph Transformations of the Sine Function Graph Transformations.
Sine, Cosine, Tangent. 8.7 Sine, Cosine, And Tangent Essential Question: How do you find the side lengths of a triangle that is not special?
Class Work 1.Sketch a right triangle that has acute angle , and find the five other trig ratios of . 2.Evaluate the expression without using a calculator.
These are two of the three Angle Sum Identities These are two of the three Angle Difference Identities.
Precalculus 4.5 Graphs of Sine and Cosine 1 Bellwork 60° 13 Find the two sides of this triangle.
Starter a 6 c A 53° 84° 1.Use Law of Sines to calculate side c of the triangle. 2.Use the Law of Cosines to calculate side a of the triangle. 3.Now find.
Trigonometric of any Angle Pg. 501 – 514 LEARNING OBJECTIVES; Use the definitions of trigonometric functions of any angle. Use the signs of the trigonometric.
Section 7-3 The Sine and Cosine Functions Objective: To use the definition of sine and cosine to find values of these functions and to solve simple trigonometric.
7.3 Trig. Functions on the Unit Circle. 7.3 CONT. T RIG F UNCTIONS ON THE U NIT C IRCLE Objectives: Graph an angle from a special triangle Evaluate.
Trig. Functions & the Unit Circle. Trigonometry & the Unit Circle VERY important Trig. Identity.
Chapter transformations on the coordinate plane.
CHAPTER 4 – LESSON 1 How do you graph sine and cosine by unwrapping the unit circle?
Do Now: If y = 2sin 2x, fill in the table below Aim: How do we sketch y = A(sin Bx) and y = A(cos Bx)? HW: Handout.
Graphing Sine and Cosine Section 4.5. Objectives Students will be able to… Use the unit circle to generate the parent graphs of sine and cosine Recognize.
Consider the function We could make a graph of the slope: slope Now we connect the dots! The resulting curve is a cosine curve.
Homework Questions. LOGS Warm-up Evaluating Logs.
TODAY IN ALGEBRA 2.0… Learning Target : You will solve triangles that have NO RIGHT ANGLE using LAW OF COSINES. Independent Practice.
Lecture 9 – Integration Basics Functions – know their shapes and properties 1 A few (very few) examples:
Evaluating Sine & Cosine and and Tangent (Section 7.4)
January 26 th copyright2009merrydavidson 2 Example Determine the amplitude, period, and phase shift of y = 2sin (3x - ) Solution: First factor out.
Holt Geometry 12-5 Symmetry 12-5 Symmetry Holt Geometry I CAN I CAN Identify line symmetry, rotational symmetry, and translational symmetry Name the pre-image.
6.3 Graphing Sine and Cosine Functions Objective: Use the graphs of the sine and cosine functions.
Graphs Cosecant Section 4.6 Objectives Graph cosecant functions Know key characteristics of the cosecant function.
Starter a 6 c A 49° 96° 1.Use the Law of Sines to calculate side c of the triangle. 2.Now find the Area of a Triangle.
1.Name the different types of triangles 2.What is the angle sum of a triangle rule? 3.What is Pythagorean Theorem and when can we use it? 4.What do you.
Trigonometry Section 7.4 Find the sine and cosine of special angles. Consider the angles 20 o and 160 o Note: sin 20 o = sin160 o and cos 20 o = -cos 160.
Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Warm up 1. Solve the triangle 10.3 Extending the Trigonometric Ratios A 12 C 15 c B.
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