Sin & Cos Graphs Section 4.5.

Slides:

Advertisements

Similar presentations

Graph: x + y = 5 1. Solve for y. 2. Make an X|Y chart. 3. Graph.

Advertisements

13.6 – The Tangent Function. The Tangent Function Use a calculator to find the sine and cosine of each value of . Then calculate the ratio. 1. radians2.30.

1 Graphs of sine and cosine curves Sections 10.1 – 10.3.

4.5 Graphs of Sine and Cosine Functions

Trig – Section 4 Graphing Sine and Cosine Objectives: To graph sine and cosine curves To find amplitude, period and phase shifts.

Graphing Sine and Cosine. Video Graphing Calculator Mode— Radians Par Simul Window— –X min = -1 –X max = 2  –X scale =  /2 Window— –Y min = -3 –Y max.

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.

Sin & Cos Graphs. Let’s explore the sine graph! _unit_circle_degrees.html

Warm UpNov. 25 th Determine whether to us the Law of Sine or Cosine and solve for the missing pieces. 1. Δ ABC with a = 12, B = 13 ˚, C= 24 ˚ 2. Δ ABC.

Transformations of Sine and Cosine Functions MHF4UI Tuesday November 13 th, 2012.

 Describe the transformations that change y = cosx into…  y = cos (x-30)  y = 3cosx  y = -cosx.

MAT 204 SP Graphs of the Sine and Cosine Functions 7.8 Phase shift; Sinusoidal Curve Fitting In these sections, we will study the following topics:

Graphs of the Sine and Cosine Functions

Nat 5 Creation of BASIC Trig Graphs Graphs of the form y = a sin xo

6.5.3 – Other Properties of Inverse Functions. Just like other functions, we need to consider the domain and range of inverse trig functions To help us.

MAT 204 FALL Graphs of the Sine and Cosine Functions 7.8 Phase shift; Sinusoidal Curve Fitting In these sections, we will study the following.

Graphing Cosecant and Secant. Using the Graphing Calculator Mode— Radians Function Sequential Window— –X min = -  –X max = 3  –X scale =  /6 Window—

Homework Questions.

Aim: How do we sketch y = A(sin Bx) and

If is measured in radian Then: If is measured in radian Then: and: -

Period and Amplitude Changes

Warm-Up 3/24-25 What are three basic trigonometric functions and the their ratios? Sine: sin  Cosine: cos  Tangent: tan 

CHAPTER 4 – LESSON 1 How do you graph sine and cosine by unwrapping the unit circle?

Starter Draw the graph of y = log(x+1) for -6≤ x ≤ 14. Draw in the asymptote Asymptote is at x = -1.

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?

Quiz 4-5 Describe how tan(x) is transformed to graph: -tan(2x)

6.3 – GRAPHING SINE AND COSINE FUNCTIONS. Periodic Function and Period  A function is periodic if, for some real number α, f(x + α) = f(x) for each x.

Do Now:. 4.5 and 4.6: Graphing Trig Functions Function table: When you first started graphing linear functions you may recall having used the following.

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.

Trigonometry Ratios.

3) 0.96) –0.99) –3/412) –0.6 15) 2 cycles; a = 2; Period = π 18) y = 4 sin (½x) 21) y = 1.5 sin (120x) 24) 27) 30) Period = π; y = 2.5 sin(2x) 33) Period.

UNIT 6: GRAPHING TRIG AND LAWS Final Exam Review.

Review of Angles. Acute Angle – Angle less than 90 degrees Right Angle – Angle that is exactly 90 degrees.

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.

X y y = sinx. x y y = cosx.

Essential Question: How do we graph trig functions, their transformations, and inverses? Graphs of Sine and Cosine.

6.2 Verifying Identities Graphically

Trigonometry Graphs Graphs of the form y = a sin xo

Find the exact values:.

Advanced Algebra Trigonometry

Unit 6: Trigonometry Lesson: Law of coSines.

Derivatives of Trig Functions

1.4 Trigonometric Functions of Any Angle

You will need a calculator and high lighter!

Graphs of Trig Functions

Derivatives of Trig Functions

Derivatives of Trig Functions

Work on worksheet with 8 multiple choice questions.

5.2 Transformations of Sinusoidal Functions

Graphs of Sine and Cosine

6-5 Translating Sine and Cosine

Graphs of Sine and Cosine Functions

Trigonometric Functions of Any Angle (Section 4-4)

State the period, phase shift, and vertical shift

Graphing sin(x) and cos(x)

Trig. equations with graphs

See A3 sheet given out in Unit 1 For more solving techniques

Sullivan Algebra and Trigonometry: Section 7.6

Trigonometry Practice Questions

Section 3 – Graphing Sine and Cosine Functions

Graphing: Sine and Cosine

8.3 – Model Periodic Behavior

Trigonometry for Angle

Trigonometric Functions

Homework Questions.

What is the radian equivalent?

Presentation transcript:

Sin & Cos Graphs Section 4.5

Sketch graphs of Sine and Cosine and their Transformations OBJECTIVE Sketch graphs of Sine and Cosine and their Transformations

RELEVANCE The universe is full of curves but straight lines are easier to measure. So trigonometry provides the basis for using triangles to measure curved space and objects. Sin and Cos graphs describe oscillations or waves.

Spaghetti Activity

Let’s explore the sine graph! http://www.mathcasts.org/gg/student/trig/sine_unit_circle_degrees.html http://www.mathcasts.org/gg/student/trig/sine_unit_circle_degrees_plus.html https://www.geogebra.org/m/zkrCZM2Y https://www.geogebra.org/m/UjjwuM8p

y = sin Ѳ

Let’s explore the cos graph! https://www.geogebra.org/m/zkrCZM2Y https://www.geogebra.org/m/UjjwuM8p

Let’s graph it on the calculator. Make sure the calculator is in radian mode Type sin(x) in y1 Press zoom trig Now let’s look at y = cos(x).

Transformations of Sine & Cosine Graphs

Transformation of sine http://www.geogebra.org/en/upload/files/english/Roger_Moss/curve_transformations.html

Write the equation of the sine function with the following features.

Write the equation of the sine function with the following features.

Homework Worksheet #1