How to Graph the Sine Function by Applying a Phase Shift and Vertical Translation

👉 Learn how to graph a sine function. To graph a sine function, we first determine the amplitude (the maximum point on the graph), the period (the distance/time for a complete oscillation), the phase shift (the horizontal shift from the parent function), the vertical shift (the vertical shift from the parent function) and the x-scale (the distance between the turns and the x-intercepts). After we have obtained these features, we plot the points on the graph and graph accordingly.
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Organized Videos:
✅ How to Graph Trigonometric Functions
• How to Graph Trigonome...
✅ How to Graph Tangent | Learn About
• How to Graph Tangent |...
✅ How to Graph Secant | Learn About
• How to Graph Secant | ...
✅ How to Graph Sine and Cosine | Learn About
• How to Graph Sine and ...
✅ How to Graph Trigonometric Functions | Learn About
• How to Graph Trigonome...
✅ How to Graph The Sine Function
• How to Graph The Sine ...
✅ How to Graph The Cosine Function
• How to Graph The Cosin...
✅ How to Graph The Tangent Function
• How to Graph The Tange...
✅ How to Graph The Cotangent Function
• How to Graph The Cotan...
✅ How to Graph Cosecant Function
• How to Graph Cosecant ...
✅ How to Graph The Secant Function
• How to Graph The Secan...
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👨‍👩‍👧‍👧 About Me: I make short, to-the-point online math tutorials. I struggled with math growing up and have been able to use those experiences to help students improve in math through practical applications and tips. Find more here: www.freemathvi...
#trig #graphing #brianmclogan

[@dimateo9800]

You deserve a fraction of my tuition fee, you make more sense than my teacher

[@angr5383]

wMathew Kaunda dame

[@zeebloxyt7728]

This guy saves my life with this math problem which is no use in my future

[@elizabethhansel2655]

Thank you so much for making these videos! My teacher doesn't teach our class in a way that any normal person could understand. All of the kids are struggling. I spent the entire Easter weekend watching your videos and I finally understood how to graph sine functions thanks to your videos. I took the test today and I got a 99%!!!!! Unfortunately, the rest of the class got C's and these are some very smart kids. I'm going to be suggesting your videos to everybody :)

[@brianmclogan]

happy to be there for you Elizabeth! keep up the hard work, and thank you for sharing the love

[@lettuce2257]

If only I had teachers like you that actually take their time to explain the lesson. Edit: Btw my brother recommended your channel, he watches your videos and it helps him a lot

[@czcensus9266]

Thank you. I have been struggling with this for 2 weeks, doing khan academy problems over and over and not getting them right. Finally this video of yours lit the light. Now I have to find one of your videos to learn to write the function from the graph. Thank you, thank you.

[@trustlaks]

Same man, they never taught it and I struggled with it

[@mamadetaslimtorabally7363]

Even as a Maths teacher myself, I find your videos fantastic Brian. Great work from you. Your videos never get outdated. They are quite a resource actually and always helpful in many ways. Thanks a lot.

[@sarahbawa736]

your videos have honestly helped me a lot in terms of math and trig functions/graphing. I pray that God blesses you abundantly for all the good work you are doimg!

[@jstewart8118]

These videos have been around for years and still help so many students (myself included). You are a great professor. Thank you.

[@brianmclogan]

you are very welcome Jake!

[@mwilson042290]

Thank you for taking the time to make this! You're a wonderful instructor- very clear and easy to follow. Thanks!

[@brianmclogan]

+mwilson042290 thank you very much! happy to be able to assist you

[@randallstanaway7846]

Thank you, Brian, for providing numerous videos on the same topic, it has really helped me to fully grasp some of these concepts!

[@Sultan_A]

“Very Good, Keep It Uuuup”

[@manpreetk.462]

I just want to say, I rarely comment on KZbin but this video helped a lot. Like many others I was having trouble with this but you made it so easy to understand. Thank you for your videos!!

[@colettepollauf5948]

Oh my god thank you so much I have my tenth grade math final soon and I have tried to get my teacher to explain to me how to graph a trig function with a phase shift so many times. I've never heard of the x-scale before and it makes SO MUCH SENSE when you put it like that. Your videos have helped me so much this year! Thanks!

[@zorinize9881]

I have to learn from you, always. My teacher barely teaches nor bothers to help struggling students. So thank yoy

[@MFblas]

Honest to god, you make my brain get this stuff in fractions of what it takes a professor in my college. I know you have heard it from me before, but thank you so so much! - Michael

[@brianmclogan]

🥰🥰🥰

[@أبوصالحالمطوع]

Thank you very much .. here after 8 years, we are watching this video and improving our self Thanks ❤

[@30_shrishtiverma97]

loved it ,I'm a indian student and u just nailed topics with ur teaching,, love nd blessings from India🙏🙏

[@noemitordoya-rivero9811]

i really appreciate your videos so much. youve saved me so many headaches and breakdowns :) my teachers lectures are pretty lengthy and wordy so its hard to keep up but you do a great job in simplifying it for someone who is terrible at mathematics!

[@stormygamingyt6734]

Hey buddy, dont say you are terrible at mathematics. Everyone is great at Mathematics. It's just the mindset that chooces whethere you are good or bad

[@Kikisnu]

These videos are so helpful!! I hope your students appreciate that they have an amazing teacher!

[@ajbasc]

omfg thank you i am struggling so hard in pre calc rn cause everything is online. this made sense i love you

[@alazander2116]

This is more informative and easy to understand than my college level course taught by a Professor

[@cheesehackerwoah9020]

Thankyou Sir, for breaking the function in detail. Now I get it.👌🏼awsome!!

[@burseebee959]

Thank you so much!! I do Kumon, and right now I'm doing this. They don't really teach you how to do it, but learning from your videos helps me to stop just estimating whatever I do. Again, thank you so much!

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You are what the world needs

[@harshdadhich9164]

5:29 cap was like ight imma head out

[@anduamlakbade3292]

keep up the hard work. you have no idea how many people you are helping!!!

[@brianmclogan]

thank you will do

[@hamsandwich7757]

i never thought to graph Horizontal phase shift like that! Thanks, I have a trig test today. Subbing

[@smd785]

He is saving my teacher’s life🥵🥵🥵🥵🥵thank you!!! My nice teacher is so terrible at teaching, I was worrying about getting a nervous breakdown...but I finally get this..I almost don’t believe it😢😢😊😊

[@anpomo6874]

wow is so cool!!!!!! I'm Korean student. I'm surprised by your teaching skill. If you upload the Korean cc you can understand better than now !!!

[@brianmclogan]

I agree, unfortunately I have so much content it is hard for me to even cc in english but would love to offer that

[@diegojoaquinsanchezalatris6670]

Brian McLogan you can add auto generated CC it’s a setting right before you upload the video

[@s.k.vi4life832]

You truly make more sense than my teacher

[@nickolasrizzato2607]

thank god for people like you.

[@jennyhernandez5830]

HEY OMG I LOVE YOU!!! Thank you for teaching me and putting these up!!!!

[@brianmclogan]

you are very welcome!

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You have helped me so much! I cannot thank you enough :)

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Thank you. I was struggling with my homework. Now, I got it.

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Better than organic chemistry tutor

[@bufdud4]

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[@Henfrig]

I always cheer when you get closer to the answer. These videos are hype af

[@andreahernandez9014]

0:46 Me as a 2-year-old trying to imitate a sheep

[@rachelrobinson114]

best professor online by far

[@plasmicgaming8830]

Thank you I've been watching videos and they help sooo much thank you for helping me get an A in college trig and on the final :)

[@justnel4]

Sweet video. Explained in 8 minutes what my professor explained in 50

[@baharosman1416]

You said if it’s inside parentheses set it equal to zero BX-C =0 Then what will be otherwise?

[@ruh_roh87]

Oh my god this is PERFECT

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You deserve extrodinary compond function of $1 and each n number of function be 1 second, and you recive your income daily. Thank you teacher.

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This fucking helped so much, youre a literal saint I love you

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Words of a wise man: "bABabAba"-Brian Mclogan

[@WNukeAPlanet]

Thank you saved my grade.

[@brianmclogan]

happy to help you out William

[@zenzon6075]

I have a test tomorrow. Please answer quickly 😢… how do you know when the phase shift is to the left of zero and not right? In other words why doesn’t it always start at zero

[@ErfanhussainKamali]

I wish you were my Methods teacher

[@edenbekele1490]

Really nice keep up

[@jennyhernandez5830]

You've helped me sooo much! In all your videos!!!

[@brianmclogan]

happy to be able to help you

[@architgupta4433]

lmao i wonder if he looks at the camera or his students

[@brianmclogan]

my students

[@mariaochoa383]

Profe Brian si yo lo tuviera a usted de profe seria recia en matematica

[@urs2350]

waayyyy better than my lecture

[@angelica6742]

OMG THANKYOU

[@dagimabebe3166]

Brian i have an assignement and i felt difficulty to do.could u help me?how could i send the question??

[@brianmclogan]

Only option I have is discord or answer on my Sunday livestream

[@dagimabebe3166]

@@brianmclogan but tomorrow ,i will submit it

[@fillertext778]

Thanks for the help!

[@antikaesart]

thanks

[@nabilaislamkhan2273]

this video helped me big time! but here is a question, if i had to plot a tan graph with the same phase shift, do I add pi/2 until i reach the 2nd x-scale? since tan graphs have a period of pi ? Please explain :((

[@brianmclogan]

well you can add pi to each critical value to obtain the next CV in the 2nd x-scale

[@nalansipahi-stallmann5263]

i like it, thank you !

[@sarayyepez3233]

How would you calculate the x-scale of y=3sin (5 (x-2pie/5))+2 and how would you graph it

[@brianmclogan]

period divided by 4

[@sarayyepez3233]

Ok so is this right the 2pie/5/4 *1/4 which equals 2pie/20 and then I simplify it and it equals pie/10

[@brianmclogan]

you got it

[@arturogonzalez6184]

I'm having trouble with placing my x-coordinates on my graph, any videos you would recommend?

[@brianmclogan]

remember you x-values are the angles, so just make sure you label the graph accordingly. I have multiple videos on this topic if you look at more examples at the end of the video

[@arturogonzalez6184]

so I should place my points with the respect of the angle of my triangle in the unit circle

[@brianmclogan]

so the way that I do it is the initial period has critical points at o, pi/2, pi, 3pi/2 and 2pi. keep adding and subtracting pi/2's to find more critical points. If you have a different period then take the period and divide it by 4 to find the new distance between each critical point. In this video the period is still 2pi, but the graph is shifted pi/6 to the left, so you will start at -pi/6 and then add/subtract pi/2 to get to the next critical points. remember that the critical points represent the max/min and x-intercepts of the graph, make sure you understand the parent graph of sine and cosine when trying to graph

[@arturogonzalez6184]

got it, thanks!

[@brianmclogan]

awesome!

[@liv3201]

This may have just saved my trig grade... whew

[@christopher_bryant]

ty

[@pugilemoltobene3708]

I was never this happy when I taught secondary math...

[@wallythedog92]

Ladies and Gentlemen!!!!!! love it

[@limesther7000]

What if the starting point is pi and your period is -2pi? Do you graph backward (to the left direction)? It's the graph of sin(pi-x)

[@brianmclogan]

sinusoid functions are continuous from (-infinity, infinity) so yes your initial period could be thought of that way but you would continue graphing both directions

[@limesther7000]

Oh..okay. Thank you sooo much!! You and your videos are helping me tremendously :D

[@mexicobasado8177]

What is this used for in real life??

[@zeebloxyt7728]

Where u get the 3 4:00

[@Hype_Machine]

Hey man remember me. We met irl. My name is philp.

[@baharosman1416]

Love you from Iraqi Kurdistan!

[@ariannaportillo7082]

makes sense!!! THANK YOU

[@brianmclogan]

+arianna portillo you are very welcome! happy to be able to help

[@1light4love]

Ok so.... I never heard it actually called an 'x-scale' and it makes sense how you apply it.... But why does your 4th x-pt from the Phase Shift not match the Period 2π?? ...... And what use IS the period value in this case then....?? (🤔Missing something)

[@mrmeowmeows7810]

VERY NICE

[@brianmclogan]

thanks!

[@favouronuoha9687]

Thank you so much

[@brianmclogan]

you are very welcome!

[@O2Jworldwide]

Très bien

[@rohandasgupta5797]

when babies make sound 0:47

[@AwsomeCookie1]

3:19 Hey, what if the phase shift was positive pi/6? do i start at that point on the graph and then add pi/2 each time until i reach the 4th x-scale? Please help me :(

[@brianmclogan]

+Raymond Hoang correct

[@AwsomeCookie1]

thank you =)

[@sophiaponce9641]

I love you

[@sraavani4542]

tyy

[@planterina_abhish]

You did -pi/6+pi/2=pi/3 but width is more than pi/2 while ploting it

[@brianmclogan]

what point in the video are you referring to?

[@ericjamesmalot7403]

What's the x scale

[@GOOSEBUMPS1234]

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[@sheila5018]

love u

[@manavbhojwani1080]

The zero shouldn't be there? Aren't u supposed to add π/2 to -π/6?

[@brianmclogan]

I am not seeing anything wrong with my work, and not sure I understand your question/s

[@manavbhojwani1080]

Its all good, thanks to you I got full in my finals!!!😁😁

[@connoryoung5297]

0:35 Noscope?

[@hasankuliyev4211]

why sin line is not touching 5pi/6?

[@brianmclogan]

because it got shifted up 1 unit

[@Butters_Stotch530]

0:48. A baby says:

[@kellycortes7106]

🙏🏻

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bah bah bah bah bah

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He's just like my teacher, fast and uncaring

[@Solbashio]

lol what

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@@Solbashio 😂😂😂

[@HadithWeekly]

0:47 .....black sheep have you any wool?....

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[@brianmclogan]

Haha

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[@cliffordmorris6091]

I left a comment but it did not get printed. If you are doing a video accept it takes time and allow each concept the time needed before you go on. I do not need the maths content but why not spend time so that those learning it can keep up. Your formula helped but put it in a box then set out each example slowly showing your thinking process not punctuated with gasps, sighs and distracting moans.

[@cliffordmorris6091]

Sorry but this guy needs to calm down . Yes his maths is okay but his antics are rather histrionic and an unnecessary distraction. Given you tube interruptions the podcast is not helpful unless you don’t actually need it and the maths is clear already. Grade E for presentation.