of 16 /16
14.1 Graphing Sine, 14.1 Graphing Sine, Cosine and Tangent Cosine and Tangent Functions Functions Algebra 2

# 14.1 Graphing Sine, Cosine and Tangent Functions Algebra 2

Embed Size (px)

### Text of 14.1 Graphing Sine, Cosine and Tangent Functions Algebra 2 14.1 Graphing Sine, 14.1 Graphing Sine, Cosine and Tangent Cosine and Tangent FunctionsFunctionsAlgebra 2 The graph of y=sin xThe graph of y=sin x The graph of y=cos xThe graph of y=cos x Characteristics of y=sinx and Characteristics of y=sinx and y=cosxy=cosxThe domain is all real numbersThe range is -1 ≤ y ≤ 1The function is periodic-the graph

has a repeating pattern. (Shortest repeating pattern called a cycle and the horizontal length is called the period) Both have a period of 2π. Characteristics of y=sinx and Characteristics of y=sinx and y=cosxy=cosxThe maximum value of y=sinx is

M=1 and occurs when The maximum value of y=cosx is

M=1 and occurs when x=2nπ.The minimum value of y=sinx is

m=-1 and occurs at The minimum value of y=cosx is

m=-1 and occurs when x=(2n+1)π

nx 2

2

nx 2

2

3 Characteristics of y=sinx and Characteristics of y=sinx and y=cosxy=cosxThe amplitude of both functions

is

Amplitude is half the height of the graph.

12

1 mM Characteristics of y=a sin bx Characteristics of y=a sin bx and y=a cos bxand y=a cos bxThe amplitude and period of the

graphs of y = a sin bx and y = a cos bx where a and b are nonzero numbers are as follows.

amplitude=

period=

a

b

2 Examples:Examples:Graph the functions

xy cos2

1

xy2

1sin

4sin2x

y Examples:Examples:Give the amplitude, period. And

five key points of the graph of each function.

xy sin

xy cos3

4sin2x

y DefinitionDefinitionFrequency- the number of cycles

per unit of time (frequency is the reciprocal of the period) Examples:Examples:A tuning fork vibrates with

frequency f=880 hertz (cycles per second.) You strike the tuning fork with a force that produces a maximum pressure of 4 pascals.◦Write a sine model that gives the

pressure P as a function of t (in seconds).

◦Graph the model. Examples:Examples:You pluck the string of a violin so

that it vibrates with frequency f = 660 hertz (cycles per second.) The force of the pluck produces a maximum pressure of 2 pascals. Write a sine model that gives the pressure P as a functions of time t (in seconds). Then give the amplitude and period of the function's graph. Tangent FunctionsTangent FunctionsThe graph of y=tanx has the

following characteristics.◦The domain is all real numbers

except odd multiples of . At , the graph has vertical asymptotes

◦The range is all real numbers.◦The graph has a period of π

2

2 Characteristics of y=a tan Characteristics of y=a tan bxbxIf a and b are nonzero real

numbers, the graph of y= a tan bx has these characteristics.◦The period is

◦There are vertical asymptotes at odd multiples of

b

b2 Examples:Examples:Graph the functions.

xy2

tan3

xy3

1tan2

1 QuestionQuestionHow do you find the amplitude,

period and vertical asymptotes of a sine, cosine, or tangent function from its equation? ##### Section 8.1: The Inverse Sine, Cosine, and Tangent …dscheib/teaching/mac1147_lecture...Section 8.1: The Inverse Sine, Cosine, and Tangent Functions The function y= sinxdoesn’t
Documents ##### Notes Over 6.4 Graph Sine, Cosine Functions Notes Over 6.4 Graph Sine, Cosine, and Tangent Functions Equation of a Sine Function Amplitude Period Complete
Documents ##### TRIGONOMETRY - WordPress.com WORKSHEET Trigonometric Ratios Indicator 1. Determining Sine, Cosine, and Tangent of angle based on ratio of right triangle. 2. Determining Sine, Cosine,
Documents ##### Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes
Documents ##### The Tangent Ratio The Tangent using Angle The Sine of an Angle The Sine Ration In Action The Cosine of an Angle Mixed Problems The Tangent Ratio in Action
Documents ##### Graph Sine, Cosine, and Tangent Functions · Graph Sine, Cosine, and Tangent Functions Later in Chapter 10, we will use sine and cosine graphs to create mathematical equations the
Documents ##### 3.2 Notes Sine and Cosine Ratios Cosine and Sine ratios · 2019. 11. 29. · 3.2 Notes Sine and Cosine Ratios Cosine and Sine ratios: - We have learned about tangent ratios. - Sine
Documents ##### Trigonometry Let’s Investigate Extension The Tangent Ratio The Tangent Angle The Sine Ratio The Sine Angle The Cosine Ratio The
Documents ##### Transparency 4. Transparency 4a Chapter 9 Right Triangles and Trigonometry Section 9.5 Sine, Cosine, Tangent
Documents ##### 8-3 8-4 Sine, Cosine and Tangent Ratios Objective Students will be able to use sine, cosine, and tangent ratios to determine side lengths in triangles
Documents ##### Hyperbolic Functions. The Hyperbolic Sine, Hyperbolic Cosine & Hyperbolic Tangent
Documents ##### 13.4 and 13.5 Basic Trig. Today we will… Find the sine, cosine, and tangent values for angles. We will also use the sine, cosine and tangent to find angles
Documents ##### Lesson 26: The Definition of Sine, Cosine, and Tangent GEOMETRY NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 26 Lesson 26: The Definition of Sine, Cosine, and Tangent This file derived
Documents ##### Section 6.4 graphs of the sine, cosine, tangent, cotangent, cosecant, and secant functions
Education ##### Inverse Hyperbolic Functions. The Inverse Hyperbolic Sine, Inverse Hyperbolic Cosine & Inverse Hyperbolic Tangent
Documents ##### 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?
Documents ##### PAHHC Handheld Electronics Page Brochure.pdf · cosine x, tangent x, arc sine x, arc cosine x, arc tangent x. Imagine an engineer designing a reclining office chair. He will allow
Documents ##### Vocabulary trigonometry trigonometric ratio sine cosine tangent inverse sine inverse cosine inverse tangent
Documents Documents