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

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wMathew Kaunda dame

[@zeebloxyt7728]

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[@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.

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

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“Very Good, Keep It Uuuup”

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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.

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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]

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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!

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THANK YOU SO MUCH YOU ANSWERED EVERY SINGLE QUESTION I HAD WITH SUCH CLARITY AND REASON

[@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

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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😢😢😊😊

[@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!!

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

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You are what the world needs

[@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

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

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

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

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The commercials interfere with my ability to follow the lesson but I like that you are doing this and I love the subject matter .

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

[@brianmclogan]

thank you will do

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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!

[@cheesehackerwoah9020]

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

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[@hamsandwich7757]

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

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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

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

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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

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

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

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[@brianmclogan]

you are very welcome!

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[@brianmclogan]

happy to help you out William

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waayyyy better than my lecture

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Really nice keep up

[@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

[@baharosman1416]

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

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

[@brianmclogan]

my students

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[@brianmclogan]

happy to be able to help you

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i like it, thank you !

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Thanks for the help!

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

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Where u get the 3 4:00

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[@brianmclogan]

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

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@@brianmclogan but tomorrow ,i will submit it

[@3ColorJaguar]

What is this used for in real life??

[@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

[@christopher_bryant]

ty

[@ariannaportillo7082]

makes sense!!! THANK YOU

[@brianmclogan]

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

[@mrmeowmeows7810]

VERY NICE

[@brianmclogan]

thanks!

[@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

[@favouronuoha9687]

Thank you so much

[@brianmclogan]

you are very welcome!

[@O2Jworldwide]

Très bien

[@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!

[@rohandasgupta5797]

when babies make sound 0:47

[@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

[@Butters_Stotch530]

0:48. A baby says:

[@connoryoung5297]

0:35 Noscope?

[@ericjamesmalot7403]

What's the x scale

[@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)

[@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?

[@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!!!😁😁

[@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 =)

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I love you

[@sraavani4542]

tyy

[@hasankuliyev4211]

why sin line is not touching 5pi/6?

[@brianmclogan]

because it got shifted up 1 unit

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

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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.