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Graphing Trigonometric Functions, Phase Shift, Period, Transformations, Tangent, Cosecant, Cosine

Not feeling ready for this? Check out Get ready for Algebra 2. Skill Summary Legend Opens a modal. Unit circle introduction. Unit circle Opens a modal. Trig unit circle review Opens a modal. Unit circle Get 3 of 4 questions to level up! Intro to radians Opens a modal. Degrees to radians Opens a modal.

Radians to degrees Opens a modal. Unit circle with radians Get 3 of 4 questions to level up! The Pythagorean identity. Proof of the Pythagorean trig identity Opens a modal. Using the Pythagorean trig identity Opens a modal.

Pythagorean identity review Opens a modal. Use the Pythagorean identity Get 3 of 4 questions to level up! Trigonometric values of special angles. Trig values of special angles Opens a modal. Trig values of special angles Get 3 of 4 questions to level up! Quiz 1. Graphs of sin xcos xand tan x. Amplitude, midline and period. Features of sinusoidal functions Opens a modal. Midline, amplitude, and period review Opens a modal. Midline of sinusoidal functions from graph Get 3 of 4 questions to level up!

Amplitude of sinusoidal functions from graph Get 3 of 4 questions to level up! Period of sinusoidal functions from graph Get 3 of 4 questions to level up! Transforming sinusoidal graphs. Amplitude of sinusoidal functions from equation Get 3 of 4 questions to level up! Midline of sinusoidal functions from equation Get 3 of 4 questions to level up!

Period of sinusoidal functions from equation Get 3 of 4 questions to level up! Quiz 2. Graphing sinusoidal functions. Sinusoidal function from graph Opens a modal.Intro Amp. Shift Phase Shift. You've already learned the basic trig graphs. We can transform and translate trig functions, just like you transformed and translated other functions in algebra.

This function has an amplitude of 1 because the graph goes one unit up and one unit down from the midline of the graph. Do you see that this second graph is three times as tall as was the first graph? The amplitude has changed from 1 in the first graph to 3 in the second, just as the multiplier in front of the sine changed from 1 to 3. This relationship is always true: Whatever number A is multiplied on the trig function gives you the amplitude that is, the "tallness" or "shortness" of the graph ; in this case, that amplitude number was 3.

For this function, the value of the amplitude multiplier A is given by 0. For this function, the value of the amplitude multiplier A is —2so the amplitude is:. Technically, the amplitude is the absolute value of whatever is multiplied on the trig function. The amplitude just says how "tall" or "short" the curve is; it's up to you to notice whether there's a "minus" on that multiplier, and thus whether or not the function is in the usual orientation, or upside-down. Do you see how this third graph is squished in from the sides, as compared with the first graph?

Do you see that the sine wave is cycling twice as fast, so its period is only half as long? In the sine wave graphed above, the value of the period multiplier B was 2. Sometimes the value of B inside the function will be negative, which is why there are absolute-value bars on the denominator.

This right- or left-shifting is called "phase shift". Because this value is added to the variable, then the shift is to the left.

Then the phase shift is:. This number is subtracted from the variable, so the shift will be to the right.Algebra 2 is the third math course in high school and will guide you through among other things linear equations, inequalities, graphs, matrices, polynomials and radical expressions, quadratic equations, functions, exponential and logarithmic expressions, sequences and series, probability and trigonometry.

This Algebra 2 math course is divided into 13 chapters and each chapter is divided into several lessons. Under each lesson you will find theory, examples and video lessons. Mathplanet hopes that you will enjoy studying Algebra 2 online with us! Equations and inequalities. How to graph functions and linear equations. How to solve system of linear equations. Polynomials and radical expressions. Quadratic functions and inequalities.

Conic Sections. Polynomial functions. Rational expressions. Exponential and logarithmic functions. Sequences and series. Discrete mathematics and probability. Share on Facebook. Search Pre-Algebra All courses. All courses. Algebra 2 Equations and inequalities Overview Solve equations and simplify expressions Line plots and stem-and-leaf plots Absolute value Solve inequalities. Algebra 2 How to graph functions and linear equations Overview Functions and linear equations Graph functions and relations Graph inequalities.

Algebra 2 How to solve system of linear equations Overview Solving systems of equations in two variables Solving systems of equations in three variables.Test and Worksheet Generators for Math Teachers. All worksheets created with Infinite Algebra 2.

Stop searching. Create the worksheets you need with Infinite Algebra 2. Basics Order of operations Evaluating expressions Simplifying algebraic expressions. Linear Relations and Functions Review of linear equations Graphing absolute value functions Graphing linear inequalities.

General Functions Evaluating functions Function operations Inverse functions. Equations and Inequalities Multi-step equations Work word problems Distance-rate-time word problems Mixture word problems Absolute value equations Multi-step inequalities Compound inequalities Absolute value inequalities. Complex Numbers Operations with complex numbers Properties of complex numbers Rationalizing imaginary denominators.

Exponential and Logarithmic Functions The meaning of logarithms Properties of logarithms The change of base formula Writing logs in terms of others Logarithmic equations Inverse functions and logarithms Exponential equations not requiring logarithms Exponential equations requiring logarithms Graphing logarithms Graphing exponential functions.

Not feeling ready for this? Check out Get ready for Algebra 2. Course summary.

### Amplitude, Period, Phase Shift and Frequency

Polynomial arithmetic. Intro to polynomials : Polynomial arithmetic Average rate of change of polynomials : Polynomial arithmetic Adding and subtracting polynomials : Polynomial arithmetic. Multiplying monomials by polynomials : Polynomial arithmetic Multiplying binomials by polynomials : Polynomial arithmetic Special products of polynomials : Polynomial arithmetic.

Complex numbers. The imaginary unit i : Complex numbers Complex numbers introduction : Complex numbers The complex plane : Complex numbers. Adding and subtracting complex numbers : Complex numbers Multiplying complex numbers : Complex numbers Quadratic equations with complex solutions : Complex numbers.

Polynomial factorization.

## Unit: Trigonometry

Factoring monomials : Polynomial factorization Greatest common factor : Polynomial factorization Taking common factors : Polynomial factorization.

Factoring higher degree polynomials : Polynomial factorization Factoring using structure : Polynomial factorization Polynomial identities : Polynomial factorization Geometric series : Polynomial factorization.

Polynomial division. Dividing polynomials by x : Polynomial division Dividing quadratics by linear factors : Polynomial division Dividing polynomials by linear factors : Polynomial division.

Polynomial Remainder Theorem : Polynomial division. Polynomial graphs. Zeros of polynomials : Polynomial graphs Positive and negative intervals of polynomials : Polynomial graphs End behavior of polynomials : Polynomial graphs.Linear Scale Log Scale DAO.

Synonyms: gamble, wager, venture, pot, ante, more. Collocations: Yeah, that's your best bet. Visit the Spanish-English Forum. Help WordReference: Ask in the forums yourself. Report an error or suggest an improvement. Your best bet would be to contact the organisers directly and ask if they still have tickets.

I bet, I'll bet interjinterjection: Exclamation--for example, "Oh no. I wouldn't bet on it. It's a fair bet exprexpression: Prepositional phrase, adverbial phrase, or other phrase or expression--for example, "behind the times," "on your own. You can bet on it. Sea lo que sea que haga el gobierno, nos va a salir dinero.

Que no te quepa la menor duda. Is something important missing. Become a WordReference Supporter to view the site ad-free. Chrome users: Use search shortcuts for the fastest search of WordReference. Please report any problems. To use our site as it is intended, you will need to download a newer browser. The browsers we support are: Internet Explorer 8 Internet Explorer 9 Internet Explorer 10 Firefox Chrome Safari Betting on auto racing has exploded in popularity in Vegas in recent years, and its appeal continues to grow.

The structure of betting on auto racing is similar to that of golf. The most basic wager involves picking the winner of a race. Typically a sports book will list 20 or more individual drivers along with a field (all others) option, at various odds. For example, Jeff Gordon may be listed at 4-1, Jeff Burton at 15-1, Casey Atwood at 100-1, etc. Auto racing matchup propositions also are available, in which two drivers are paired against each other in a head-to-head wager, with a betting line on each driver set by the oddsmaker.

The driver with the better finish in the race wins the matchup. To bet on baseball, tell the ticket writer the bet number of the team you wish to bet and the amount you wish to wager. If your team wins the game, you win. The payout varies according to the odds posted.

Baseball odds are shown using a "Money Line. A "minus" (-) preceding the number indicates the team is a favorite. You can arrive at the underdog's price by looking at the favorite's line. Dime lines are slowly disappearing as sports books look to make a larger profit during what is traditionally the slowest betting season. Several books still offer dime lines. Money lines change constantly. The listed money line the time you make your bet may be different from the money line when the game starts.

The listed line on your ticket is your official odds, unless starting pitcher is changed. This is explained later. You may wager that the total score of the game will be more or less than the number listed. It makes no difference which team wins.

Simply add the final scores of each team.Luke Rockhold unseated previously undefeated Chris Weidman in the main event to become the seventh middleweight champion in UFC history.

Baskow Light Heavyweight Title fighter Jon Jones trades punches with opponent Daniel Cormier as they battle during their UFC182 fight at the MGM Grand Garden Arena on Friday, January 2, 2014. Full comments policy Conor McGregor stops Jose Aldo for fastest finish in title fight history Conor McGregor became more than UFC featherweight champion with his 13-second knockout victory over Jose Aldo.

Main Card Results WinnerLoserMethod Conor McGregorJose AldoKnockout Luke RockholdChris WeidmanTKO Yoel RomeroRonaldo "Jacare" SouzaSplit Decision Demian MaiaGunnar NelsonUnanimous Decision Max HollowayJeremy StephensUnanimous Decision DateEventHeadlining MatchLocation October 7 UFC 216 Tony Ferguson vs. Kevin Lee Las Vegas: T-Mobile Arena October 19 Golden Boy Boxing on ESPN Gabriel Rosado vs. Glen Tapia Las Vegas: Park Theater October 21 UFC Fight Night 118 Donald Cerrone vs.

Darren Till Gdansk, Poland October 28 UFC Fight Night 119 Lyoto Machida vs. Derek Brunson Sao Paulo November 4 UFC 217 Michael Bisping vs.

McGregor fight Written by Nikhil Sonnad August 26, 2017 We're both gonna be rich anyway. But how much they win or lose depends on the betting odds for the fight between Floyd Mayweather and Conor McGregor, which have changed dramatically since they were first recorded. Mayweather has an inhuman 49-0 record in boxing matches, while McGregora mixed martial arts and UFC fighterhas not fought any pure boxing matches professionally. That imbalance has made Mayweather a massive favorite, but since the fight date was announced in June, the odds have tightened.

### Graphing Trigonometric Functions

Those numbers require some explanation of the weird betting odds system used in the United States, called moneylines. So the more negative the moneyline for an outcome, the more likely betting markets think that outcome is.

The biggest winners, of course, will be Mayweather and McGregor, who, win or lose, stand to earn hundreds of millions of dollars. McGregor: The latest odds and how the betting moneyline has changed over time","facebookTitle":"How the odds have changed for the Mayweather vs.

McGregor fight","facebookDescription":"The moneylines for the match are getting closer and closer. We'll be back soon. Vegas reveals the betting odds Contributed by Jordan Zakarin Sep 6, 2017 Share This Post Shared 2 Comments Once again, Lucasfilm has removed a director from a Star Wars film. After booting Chris Miller and Phil Lord from the Han Solo spinoff this summer, and sidelining Gareth Edwards for big reshoots and edits on last winter's Rogue One, the latest forsaken filmmaker is Colin Trevorrow, who will no longer be at the helm of the untitled Episode IX.

By now we know the drill: Lucasfilm releases a statement (or not, in the case of Edwards), fans speculate as trade reporters scramble for insight, and then a few days later, a new director is named. Now there's a new wrinkle in the process: During that speculating phase, people can put their money where their fan theories are by placing bets on who will fill the biggest job opening in the galaxy.

Raphael Esparza works for Doc Sports and My Bookie, and lays out lines on not only sports, but pop culture events as well. He's put odds on various Game of Thrones twists, and even Rey's parentage. Abrams boy, and has great experience with visual effects.

She would add a female influence that I think Star Wars IX will have. Shana O'Neil Sep 12, 2017 Star Wars: Episode IX opinion Star Wars: Dissecting the director changes in a galaxy far, far away Lucas Siegel Sep 5, 2017 Star Wars Star Wars: Episode IX Star Wars: Episode IX lands new writer Matthew Jackson Aug 1, 2017 J. Abrams Star Wars: Episode IX J.

Abrams says he never intended on returning to Star Wars, so what changed. PreviewsWatch Artists Sketch All Comics Latest Stories X-Men filmmakers look back at what went wrong San Diego Comic-Con has won its trademark lawsuit against Salt Lake Comic Con Jessica Jones is back on the job with new trailer and release date.

Fangrrls is about kicking down doors, breaking boundaries and celebrating female fans with fun, witty and entertaining content.

Vegas reveals the betting odds Contributed by Jordan Zakarin Sep 6, 2017 Share This Post Once again, Lucasfilm has removed a director from a Star Wars film. Shana O'Neil Star Wars: Episode IX opinion Star Wars: Dissecting the director changes in a galaxy far, far away Lucas Siegel Star Wars Star Wars: Episode IX Star Wars: Episode IX lands new writer Matthew Jackson J.

Wall explains interviewing Beal 1:06 Matt Niskanen tips in game-winner against Rangers 1:59 Beal stays hot in road win over Suns 1:32 Bradley Beal couldn't use his phone after 51-point game 1:51 Junkies try to dissect Dan Patrick's Cousins, receivers comment After going 0-2 against the Steelers and the Cowboys, the Redskins are headed to New York for another NFC East game, this week against the Giants. This week's game is a critical one, so much so that John Feinstein said if the Redskins don't win, their season is "basically over.

How to Watch: Redskins Kickoff airs at Noon on CSN Mid-Atlantic.