Pg. 346 Homework Pg. 346#27 – 41 odd Pg. 352 #7 – 12 all Study Trig Info!! Next Quiz is Monday! #1max = 4, a = 4#2max = 1, a = 1 #3max = 15, a = 15#4max.

Slides:



Advertisements
Similar presentations
Trig Graphs. y = sin x y = cos x y = tan x y = sin x + 2.
Advertisements

4.5 Graphs of Sine and Cosine Functions AmplitudePeriodTranslations.
Starter.
Graphing Sine and Cosine Functions
We need to sketch the graph of y = 3sin(5t+90)
Pre calculus Problem of the Day Homework: p , 11, 17, 23, 25, 35, 39, 43, 49 Find the indicated function values for the following:
Objective Recognize and graph periodic and trigonometric sine and cosine functions.
4.4 Graphs of Sine and Cosine: Sinusoids. By the end of today, you should be able to: Graph the sine and cosine functions Find the amplitude, period,
4.5 Sinusoidal Graphs Sketching and Writing Equations.
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.
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 Sine and Cosine Five Point Method. 2 Plan for the Day Review Homework –4.5 P odd, all The effects of “b” and “c” together in.
Pg. 346/352 Homework Pg. 352 #6, 8 – 11, 15 – 17, 21, 22, 24, 27, 28, 30 – 32.
Extra 5 pt pass if…. You can find the exact value of cos 75˚ with out a calculator. Good luck!!
Homework: Graphs & Trig Equations 1.State the amplitude, period & then sketch the graph of (a) y = 3 cos 5x + 10 ≤ x ≤ 90 (b)y = ½ sin 2x0 ≤ x ≤ 360.
Today’s Date: 9/13/ Solving Inequalities in 1 Variable & 2.2 Solving Combined Inequalities.
Graph Transformations (I)f(x), f(x) +/- k, f(x +/- k)See Handout Example The following graph shows y = g(x). Make sketches of (a) y = g(x) + 3 (b) y =
6.5 – Inverse Trig Functions. Review/Warm Up 1) Can you think of an angle ϴ, in radians, such that sin(ϴ) = 1? 2) Can you think of an angle ϴ, in radians,
Homework Questions.
The Wave Function Heart beat Electrical Many wave shapes, whether occurring as sound, light, water or electrical waves, can be described mathematically.
This is the graph of y = sin xo
Tips For Learning Trig Rules. Reciprocal Rules Learn:
Period and Amplitude Changes
Chapter 4.4 Graphs of Sine and Cosine: Sinusoids Learning Target: Learning Target: I can generate the graphs of the sine and cosine functions along with.
4.2 Graphing Sine and Cosine Period. 4.1 Review Parent graphs f(x) = sin(x) and g(x) = cos(x) For y = a*sin(bx - c) + d and y = a*cos(bx - c) + d, the.
4.3 Period Changes and Graphs other Trig Functions
2.6 Graphs of the Sine and Cosine Functions xxy = sin x 00=SIN(B2) π/6=PI()/6=SIN(B3) π/3=PI()/3=SIN(B4) π/2=PI()/2=SIN(B5) 2π/3=B5+PI()/6=SIN(B6) 5π/6=B6+PI()/6=SIN(B7)
Pg. 335 Homework Pg. 346#1 – 14 all, 21 – 26 all Study Trig Info!! #45#46 #47#48 #49Proof#50Proof #51+, +, + #52 +, –, – #53–, –, + #54 –, +, – #55 #56.
Cofunction Identities
6.4.2 – Graphing Transformed Trig Functions. Based on the previous 2 days, you should now be familiar with: – Sin, Cos, Tan graphs – 3 different shifts:
Pg. 408/417/423 Homework Study for Quiz!! #34* R.H.S by cos x#35see verification worksheet #36 #172sinθcosθ + cosθ#182sinθcosθ + cos 2 θ – sin 2 θ (ans.
1.6 Graphing Trig Functions Yesterday we focused on the Unit Circle, today we start graphing Trigs.
Amplitude, Period, and Phase Shift
Pg. 346/352 Homework Pg. 352 #13 – 22, 45, 46 Study for trig memorization quiz. Hand draw graphs of the six trig functions and include domain, range, period,
Graphs of Tangent, Cotangent, Secant, and Cosecant
What is the symmetry? f(x)= x 3 –x.
14.1, 14.2 (PC 4.5 & 4.6): Graphing Trig Functions HW: p.912 (3-5 all) HW tomorrow: p.913 (6, 10, 16, 18), p.919 (12-16 even) Quiz 14.1, 14.2: Tuesday,
Exam Review Chapters Q. Find the exact value of sin 240° sin 240°
Trigonometric Graphs.
6.3 Graphing Trig Functions
Pg. 352 Homework Study, Study, Study!! **Test Wednesday!!** #15#36-120°, -2π/3 #2368°, 112°#4723°, 23π/180 = 0.40 #5175°#290.36, 0.93, 0.38 #371.28, 1.27,
Periodic Functions. A periodic function is a function f such the f(x) = f(x + np) for every real number x in the domain of f, every integer n, and some.
Solving for (3 Ways). Examples Without using a calculator, what angle(s) would satisfy the equation ?
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.
Check Your Homework Answers with a Partner & Around the Room… Unit Circle Quiz Day!
Trigonometric Graphing Day 1 What do the graphs look like?
4.5 Graphs of Trigonometric Functions 2014 Digital Lesson.
Top 10 of Set 1 Review Domain and Range Inverses Odd and even rules for a function Questions: 2,3,7,10,11,12,13,20,23,31.
Warm up Use the Pythagorean identity to determine if the point (.623,.377) is on the circumference of the unit circle Using Pythagorean identity, solve.
Sin x = Solve for 0° ≤ x ≤ 720°
Graphs of the form y = a sin x o Nat 5 Graphs of the form y = a sin bx o Phase angle Solving Trig Equations Special trig relationships Trigonometric Functions.
Section 3.5 Trigonometric Functions Section 3.5 Trigonometric Functions.
1. Be able to write down the period and amplitude from a graph 2. Be able to state the period and amplitude from an equation 3. Be able to write down equation.
5.3 Part 1 Trig Graphs A function is periodic if its values repeat in a cycle. Sin and Cos functions repeat their values in a regular fashion. Since.
Trigonometric Graphs 6.2.
Translation Images of Circular Functions
Graphs of Trig Functions
Graphing Trigonometry Functions
Trigonometric Graphs 1.6 Day 1.
Chapter 4: Lesson 4.6 Graphs of Other Trig Functions
TRIGONOMETRIC GRAPHS.
The Chain Rule Section 4 Notes.
Graphing Trig Functions
State the period, phase shift, and vertical shift
Graphing sin(x) and cos(x)
Look over Unit Circle! Quiz in 5 minutes!!
F(x) = a trig (bx - c) + d.
sin x cos x tan x 360o 90o 180o 270o 360o 360o 180o 90o C A S T 0o
Warm-up: For the following equation, give the required values and graph. For the shifts, give direction as well as units of translation. If there is.
Homework Questions.
Presentation transcript:

Pg. 346 Homework Pg. 346#27 – 41 odd Pg. 352 #7 – 12 all Study Trig Info!! Next Quiz is Monday! #1max = 4, a = 4#2max = 1, a = 1 #3max = 15, a = 15#4max = 3, a = 3 #5 max = 5, a = 5 #6max = 12, a = 12 #7 D: ARN; R [-1, 1], 2π/3#8D: ARN; R [-1, 1], 2π/7 #9 D: ARN; R [-4, 4], 2π/5 #10D: ARN; R [-2, 2], 2π/9 #11D: ARN; R [-3, 3], π #12D: ARN; R [-6, 6], 2π/9 #13D: ARN; R [-1, 1], 2π/3 #14D: ARN; R [1, 3], 2π #21[0, π] x [-2, 2]#22 [0, 4π] x [-2, 2] #23[0, 4π] x [-3, 3] #24 [0, 6π] x [-2, 2] #25[0, 10π] x [-4, 4] #26[0, 8π] x [-4, 4]

6.3 Graphs of sin x and cos x Amplitude The amplitude of f(x) = asin x and f(x) = acos x is the maximum value of y, where a is any real number; amplitude = |a|. State the amplitude: y = 4sin(6x) y = -3cos(0.25x) Period Length One period length of y = sin bx or y = cos bx is State the period length: y = 4sin(6x) y = -3cos(0.25x)

6.3 Graphs of sin x and cos x Horizontal Shifts Remember our cofunctions and why they were true? Well, they are true with graphing too! The cofunctions lead into shifts. If a value is inside with the x, it is a horizontal shift left or right opposite the sign. If it is outside the trig, it is up or down as the sign states. Symmetry of sin x and cos x Looking at the Unit Circle to help, think about the difference between the following: sin (-x) = -sin (x) cos (-x) = cos (x)

6.3 Graphs of sin x and cos x Examples Graph one period of the following: y = 4sin x y = -3cos (2x) y = sin (0.5x) + 1 y = 2sin (x – 1) Solve for the following: sin x = 0.32 on 0 ≤ x < 2π cos x = on 0 ≤ x < 2π sin x = on 0 ≤ x < 2π cos x = 0.65 on 0 ≤ x < 2π

6.4 Graphs of the Other Trig Functions Graphing tan x What are the values to “worry about” with tan x? What does a function do at a vertical asymptote? Graph tan x. Period Length of tan x How long does it take for tan x to take on all its possible values? π!!