What is the amplitude and period of. Amplitude 7 Period 12π.

Slides:

Advertisements

Similar presentations

Solving Right Triangles Essential Question How do I solve a right triangle?

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.

10.5 Write Trigonometric Functions and Models What is a sinusoid? How do you write a function for a sinusoid? How do you model a situation with a circular.

EXAMPLE 1 Solve a multi-step problem

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

TRIGONOMETRY, 4.0: STUDENTS GRAPH FUNCTIONS OF THE FORM F(T)=ASIN(BT+C) OR F(T)=ACOS(BT+C) AND INTERPRET A, B, AND C IN TERMS OF AMPLITUDE, FREQUENCY,

Warm UP 1) Name the following parent graph: 2) Where is a point of inflection(s) for the function y=cos(x) on the interval [0 o, 360 o ]? 3) On what subinterval(s)

Translations of Sine and Cosine Functions

4-4 Graphing Sine and Cosine

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:

EXAMPLE 3 Simplify an expression Simplify the expression cos (x + π). Sum formula for cosine cos (x + π) = cos x cos π – sin x sin π Evaluate. = (cos x)(–1)

Simplify an expression

Quiz Find a positive and negative co-terminal angle with: co-terminal angle with: 2.Find a positive and negative co-terminal angle with: co-terminal.

Graphs Transformation of Sine and Cosine

Unit 3 Graphing Review. Let’s graph some trig functions!

Graphs of the Sine and Cosine Functions

The Inverse of Trigonometric Functions

8.3 Solving Right Triangles

Graphs of the Sine and Cosine Functions Section 6.

This is the graph of y = sin xo

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

Trigonometric Functions

Friday, February 5 Essential Questions

Section 8-2 Sine and Cosine Curves. Recall… The Sine Graph.

10.2 Translate and Reflect Trigonometric Graphs

Amplitude, Period, and Phase Shift

EXAMPLE 4 Combine a translation and a reflection Graph y = –2 sin (x – ). 2 3 π 2 SOLUTION STEP 1Identify the amplitude, period, horizontal shift, and.

14.1 Trig. Graphs.

Section 4.5 Graphs of Sine and Cosine. Overview In this section we first graph y = sin x and y = cos x. Then we graph transformations of sin x and cos.

1 Example 1(a) Sketch the graph of f(x) = 3sin x. Solution The graph of f plots the point (x,3sin x) at three times the height of the point (x,sin x) on.

13.5 – The Cosine Function.

13.7 I NVERSE T RIGONOMETRIC F UNCTIONS Algebra II w/ trig.

Trig Review. 1.Sketch the graph of f(x) = e x. 2.Sketch the graph of g(x) = ln x.

Review Sticky ball!. Problem 1 Problem 2 Solve for x:

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.

W ARM UPM AY 14 TH The equation models the height of the tide along a certain coastal area, as compared to average sea level (the x-axis). Assuming x =

REVIEW OF UNIT 4.

Simple Trigonometric Equations The sine graph below illustrates that there are many solutions to the trigonometric equation sin x = 0.5.

Mathematics 2 Module 4 Cyclic Functions Lecture 3 Making Waves.

EXAMPLE 1 Graph a vertical translation Graph y = 2 sin 4x + 3. SOLUTION STEP 1 Identify the amplitude, period, horizontal shift, and vertical shift. Amplitude:

Solving Right Triangles Use trigonometric ratios to find angle measures in right triangles and to solve real-world problems.

Algebra II Honors Problem of the Day Homework: p a,b,g,3c,d,5,9,13,29,41,43 After watching the video graph y = cos t and y = sin t. graphing the.

Periodic Function Review

Section 4.5 Graphs of Sine and Cosine. Sine Curve Key Points:0 Value: π 2π2π π 2π2π 1.

Graphing Trig Functions Review Whiteboard Activity.

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.

Describe the vertical shift in the graph of y = -2sin3x + 4. A.) Up 2 B.) Down 2 C.) Up 4 D.) Down 4.

12.7 Graphing Trigonometric Functions Day 1: Sine and Cosine.

Chapter 6 Section 6.4 Translations of the Graphs of Sine and Cosine Functions.

4.1 and 4.2 Sine Graph Sine & Cosine are periodic functions, repeating every period of 2  radians: 0 x y 180   90  /  /2 1 y = sin (x)x.

1° = 60 ′ 1 ′ = 60 ″ Convert 50°6 ′ 21 ″ 50° + 6 × (1/60)° + 21 × (1/60) × (1/60)° = ° Convert to degrees 21° +.256(60 ′ ) 21° ′

Section 3.5 Trigonometric Functions Section 3.5 Trigonometric Functions.

Translations of Trigonometric Graphs LESSON 12–8.

4.3 Right Triangle Trigonometry Objective: In this lesson you will learn how to evaluate trigonometric functions of acute angles and how to use the fundamental.

Chapter 6 Section 6.3 Graphs of Sine and Cosine Functions.

Drawing Trigonometric Graphs.. The Basic Graphs. You should already be familiar with the following graphs: Y = SIN X.

6-6. “A” is for amplitude. This is ½ the distance from the highest and lowest value. So……. Highest Value – Lowest Value 2.

QUIZ PRACTICE Trigonometric Angles Graphing Sine and Cosine

Sinusoidal Modeling I. Getting the trig equation from data points.

Unit #6: Graphs and Inverses of Trig Functions

Sinusoidal Modeling I. Getting the trig equation from data points.

Chapter 4: Lesson 4.5 Graphs of Sine and Cosine Functions

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

State the period, phase shift, and vertical shift

Writing Trig Functions

Warm-up 1) write 3 positive and 3 negative solutions to the equation:

Presentation transcript:

What is the amplitude and period of

Amplitude 7 Period 12π

Write an equation for a cosine wave with a phase shift of -3 and a period of 3π/2.

y=cos(4/3(x+3))

Find the phase shift, period, amplitude, and vertical shift of

phase shift -3π/10 period π/5 amplitude 5 vertical shift 3

Find all solutions to between 0 o and 720 o, round your answers to the nearest hundredth.

45.58 o o o o

Find the general solution to in radians. (No Calculator)

π/3+2πn -π/3+2πn

The function f(x) = cos -1 (x) is defined for what angles?

0≤x≤π

Identify the functions that are graphed below.

y=sec(x) y = sin -1 (x)

What is the maximum and minimum of

Maximum 11 Minimum 1

Calculate the following without a calculator

π/3

Calculate the following without a calculator

5π/6

Calculate the following with a calculator

Graph

Solve 6 sin (5x) + 3 = 4 Find the general solution in radians

πn/ πn/5

Find an equation for the following situation. In one city in the southern hemisphere, the lowest average temperature is in April when it is 42 o. The highest average temperature occurs in October and is 82 o. Find an equation for a cosine wave that matches the situation.

y = 20 cos (π/6(x - 10))+62

Between what two times is the average temperature first above 78 o ?

8.771 and months

Simplify the following (cot x)(sec x)(sin x) - (sin x)(tan x)(cos x)

cos 2 x

Calculate cos(465 O ) without a calculator

Calculate sin(-5π/12) without a calculator

Given that sin x = 5/8 and that π/2 < x < π find the following ratios without a calculator cos x sin -x cos 2x

√39/8 -5/8 11/64