You have 5 minutes to get ready for the unit circle quiz!

Slides:

Advertisements

Similar presentations

Graphing Trig Functions

Advertisements

7.8 Sinusoidal Graphs.

Aim: Graphs of y = sin x and y = cos x Course: Alg. 2 & Trig. Aim: What do the graphs of Trig functions look like? Do Now: You and a friend are the last.

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.

Graphing Sine and Cosine. Periodic function: A function which has a graph that repeats itself identically over and over as it is followed from.

4.5 Sinusoidal Graphs Sketching and Writing Equations.

6.4.1 – Intro to graphing the trig functions. Similar to other functions, we can graph the trig functions based on values that occur on the unit circle.

Graphs of Trig Functions

Graphs of the Sine and Cosine Functions

Homework Questions.

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.

6.2 Cofunction and Double-Angle Identities Fri Dec 5 Do Now Simplify (sinx + cosx)(sinx – cosx)

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.

Section 5.3 Trigonometric Graphs

6.4 Amplitude and Period of Sine and Cosine Functions.

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,

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

Trigonometric Graphs.

6.3 Graphing Sine and Cosine Functions. Periodic Functions A periodic function is a function with a repeating pattern this includes sin and cos graphs.

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.

Graphing Sine and Cosine Amplitude Horizontal & Vertical Shifts Period Length.

Section 1.5 Trigonometric Functions

November 29, 2012 Period and Amplitude of the Sine and Cosine Functions Warm-up: Finish Sine and Cosine Function Activity (15 minutes) HW 4.5: Pg

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.

UNIT 6: GRAPHING TRIG AND LAWS Final Exam Review.

GRAPHING SINE/COSINE FUNCTIONS Section 5.4. How to find the amplitude and period when given the graph of a function. 2.The period is the distance traveled.

Module 6.4 Graphing Sine and Cosine Functions with Different Amplitudes and Periods.

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.

5.1 Graphing Sine and Cosine Functions

MATH 1330 Section 5.4.

Transformations of the Graphs of Sine and Cosine Functions

MATH 1330 Section 5.2.

Trigonometric Graphs 6.2.

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

Transformations of the Graphs of Sine and Cosine Functions

2.7 Sinusoidal Graphs; Curve Fitting

Graphs of Trig Functions

Warm Up Evaluate Find the measure of the reference angle for each given angle that would be on the unit circle ° 5.

MATH 1330 Section 5.4.

MATH 1330 Section 5.1.

Transformations of the Graphs of Sine and Cosine Functions

MATH 1330 Section 5.2.

Trigonometric Graphs 1.6 Day 1.

Amplitude, Period, and Phase Shift

Graphs of Trigonometric Functions

TRIGONOMETRIC GRAPHS.

MATH 1330 Section 5.2.

Graphing Trig Functions

Warm Up Get your Spaghetti Sine projects off the shelf and return to your partner. Do not continue working on the project, rather, answer the questions.

Review from Tuesday, evaluate

MATH 1330 Section 5.2.

Graphs of Trigonometric Functions

Graphing sin(x) and cos(x)

Warm Up Get your Spaghetti Sine projects off the shelf and return to your partner. Do not continue working on the project, rather, answer the questions.

Trig. equations with graphs

Graphing Trig Functions

Look over Unit Circle! Quiz in 5 minutes!!

Warm Up Get your Spaghetti Sine projects off the shelf and return to your partner. Do not continue working on the project, rather, answer the questions.

Trigonometric Functions

Graphs of Trigonometric Functions

5.1 Graphing Sine and Cosine Functions

Graphing: Sine and Cosine

8.3 – Model Periodic Behavior

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.

T5.1b To Graph the Cosine Curve Do not say the answers out loud!!!

Graphing Trig. Functions

7.3 Periodic Graphs & Amplitude Objectives:

Trigonometric Functions

Homework Questions.

Presentation transcript:

You have 5 minutes to get ready for the unit circle quiz!

Graphing Trig Functions

Sine Graph of y = sin(x) Starts at the origin. 1 -4π -3π -2π -π π 2π π 2π 3π 4π Starts at the origin. -1

Cosine Graph of y = cos(x) Starts at the max. 1 -4π -3π -2π -π π 2π 3π π 2π 3π 4π -1

Period of a Function When the values of a function regularly repeat themselves, we say that the function is periodic. The period of a function is the length of the piece of the graph that repeats itself.

π 2π 3π 4π 5π 6π The period of y = sin(x) is 2π because that is the length of the piece that repeats.

Amplitude Amplitude is the distance from the midpoint to the highest and lowest point of the function. (Half the distance from the max to the min.) Always measure the amplitude from “sea level.” Sea level changes as the center of the graph moves up and down. 1 -4π -3π -2π -π π 2π 3π 4π -1

Sine vs. Cosine Graphs Both graphs have a period of 2π. 1 -4π -3π -2π -π π 2π 3π 4π -1 y = sin(x) starts at 0. Both graphs have a period of 2π. Both graphs have an amplitude of 1. 1 y = cos(x) starts at 1. -4π -3π -2π -π π 2π 3π 4π -1

Find the period of each graph: π 2π 3π 4π 5π 6π π 2π 3π 4π 5π 6π π 2π 3π 4π 5π 6π

Find the amplitude of each graph: 1 -1 π 2π 3π -2 5 -3 π 2π 3π π 2π 3π -16

y = asin(bx) y = acos(bx) Amplitude of the graph = a Period of the graph = b is not the period! We evaluate this expression with different values of b to find the period of a function.

Example 1: Determine the period and amplitude of each trig function: y = 7cos(2x) y = -8sin(3x) y = ¼cos(6x) y = -sin(πx)

Example 2: Determine the period and amplitude of the function Example 2: Determine the period and amplitude of the function. Then, graph it! y = 5sin(2x)

Example 3: Determine the period and amplitude of the function Example 3: Determine the period and amplitude of the function. Then, graph it! y = ⅔cos(4x)

Example 4: Determine the period and amplitude of the function Example 4: Determine the period and amplitude of the function. Then, graph it! y = -16sin(x)

Video help https://www.youtube.com/watch?v=kiuV-DAlopE https://www.youtube.com/watch?v=yR7y8hyOpDU https://www.youtube.com/watch?v=vHYI93UV5Kg