Graphing Sine and Cosine Functions with Transformations (Multiple Examples)

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Learn how to graph sin and cos in this video math tutorial by Mario's Math Tutoring. We go through 7 examples as well as show how to graph the basic sine and cosine graph using the unit circle. We discuss the transformations such as the phase shift, vertical shift, amplitude and period as well as when the graph is reflected over the x-axis. We discuss how to find the period and how to find the scale for your graph.
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Опубликовано:

5 янв 2020

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Комментарии : 128

@mark8877 3 года назад

I’m a professional full-time math tutor, and without any caveats I can say that Mario’s tutorial videos are some of the best on RU-vid. No one is as clear, concise, or thorough in their explanations as Mario. I often recommend/send his videos to my students. The only thing I have against this video is that the period of a sin or cos function is 2pi divided by the absolute value of b, rather than just b. Regardless, this did not matter for this particular video because all b values were positive, and overall it’s still an excellent video and explanation.

@zambo8610 2 года назад

Hi, in a lot of coarses (mine as well) is b defined as a strictly postitve number. So I think that he also follows that rule

@rebeccasmerdal7784 2 года назад

I 100% agree! I am a full-time professional Math tutor as well, and refer my students to this guy! The videos are on point, and I like how he provides lots of different examples for students to gather a full bodied understanding from 👌

@ninadee9753 Год назад

Hi! Can you explain why the period = 2i/b? I am so lost with that

@lukebowman9260 Год назад

@@ninadee9753 the period of the parent functions of sin and cos is 2pi. So, in order to find the new period you have to divide 2pi by the number in front of the x value.

@salmanhamen 7 месяцев назад

Are you sure😅

@blackforestdruid Год назад

I felt very overwhelmed by this in my trig class but your videos saved the day! I got a 38/40 on the quiz for graphing trig functions. Seriously, thank you so much Mario! Your videos are excellent.

@MariosMathTutoring Год назад

Awesome! Glad my video helped you!

@DanielA-pg2no 4 года назад

Genuinely saving my grade I love you Mario

@MariosMathTutoring 4 года назад

Glad my video helped you Daniel!

@niallspotat0e823 3 года назад

i think your method of teaching how to graph considering the phase shift and period is the best one I've seen. that whole thing about making your new origin really helps

@sweethmv 19 дней назад

I wish that I had teachers like you in school. Your voice is calming. Your delivery of information is smooth and simple. Thanks. You have made college for me possible.

@MariosMathTutoring 19 дней назад

You're very welcome!

@jasonwolters7306 2 года назад

This man is the GOAT. If my teacher could explain this 1/2 as well as you could I would have an A+ in the class

@coachjeffnac 3 года назад

Thank you for the variety of examples! The last one is the one I've been stuck on and was explained so easily and clearly.

@chandra68 3 года назад

One of the best videos on trigonometric transformation. Concept and problem solving were taught in a simple yet effective fashion. Hats off to your teaching abilities. Thankyou and weldone.

@sarafinamcinnis9990 2 года назад

thank you so much mario. i've been trying to graph this one sin one for hours and I finally got it because of you!

@andrehardaman9375 3 года назад

You have no idea how much this helped me, I was so lost before and this helped me understand and complete my homework assignment. Thank you so much.

@georgeh1352 20 дней назад

Had to learn advanced Trigs much later in life, this video has filled in some gaps of my knowledge. I'm 75yrs old, so still learning out of curiousity and keeping the mind alert. Making the concept of a 'new origin' is the 'penny dropper', I guess that's the difference between a Teacher that can teach a subject and one that can't. Many thanks for your video.

@MariosMathTutoring 20 дней назад

You’re welcome!

@ahmadjamal2320 2 года назад

One of the best videos I have seen so far. Keep up the good work mate.

@ddahstan6876 2 года назад

Super duper easy to understand and follow. Love the Period/4 to nail down the graph at the get-go... and the rest can pursue to the rhythm.

@durdonabakhtiyor2534 2 года назад

Wow, it was a fantastic explanation Sir, thank you a lot. Why I didn't watch it earlier. I have watched so many tutorials on the RU-vid channel but yours is one of the best which I have ever seen 👍👍👍👍

@rodneysteenekamp8924 3 года назад

I was really battling with this. Your video helped me alot, the work makes much more sense to me now. thank you!

@bluecat7431 2 года назад

Thank you so much! This was one of the topics I was really struggling on.

@theman7050 2 года назад

This is brialliant and exactly what I was looking to understand for generative art. Thank you

@rkumaresh 2 года назад

Thanks so much. You have cleared most of my doubts in this topic of graphing the sine and cosine functions. I could watch it as many times as and when I require them. Regards Tutor Kumaresh

@jakahifreeman6614 3 года назад

you’re the best at explaining things helped a lot thank you!

@gutierrezjeffryv.7649 6 месяцев назад

you're such a really great professor I have ever found here in youtube. Your explanation is well-delivered and comprehensible.

@MariosMathTutoring 6 месяцев назад

Thanks! 😃

@RaffaelloLorenzusSayde 2 года назад

To clear the confusion for some people: We are looking for the period in 1 quadrant in a total of 4 quadrants (horizontally) of a unit circle (portrayed unto a sinusoidal graph), so that would be the equation 1/4 quadrants times the period 2pie/|b| = per 1/4rth of a period. The starting point will be d and thus, we will add by the 1/4rth of a period each time. Also, he might mutliply the denominator by common multiples of the 1/4rth period and the starting point d to get the LCD of both matching denominators (only if one or both are fractions). Btw, every curve is a quadrant.

@ryanlorenti469 3 года назад

you’re an amazing teacher bro stg

@Op_Hunter5 5 месяцев назад

Thank you mario.I really appreciate your mathematics technique with us.

@MariosMathTutoring 5 месяцев назад

Glad you like them!

@soybean_TM Год назад

Thank you so much Mario! I found this video very helpful

@metookwok6545 Месяц назад

thank you sir ! you save my math and my life🥲🥲🥲

@yojacq 2 года назад

God bless you man this is so much easy to understand and follow

@curtpiazza1688 2 года назад

Excellent presentation...I wish I had you 40 years ago!

@yasmineyasmine8059 2 года назад

Thank you very much, you saved my grades!!!

@MrBeafyYT 3 года назад

thank you so much for this video, helped me out a lot!

@user-yt6hw2yb7p 2 года назад

I have an exam and you saved my time with your perfect explanation. Thank you

@arslanmoghal5472 Год назад

Very well explained.. Good video 👍👍, thank you

@learnwithjustintoday Год назад

That's a really awesome tip at 3:12 Thank you!

@ferozdba 10 месяцев назад

thank you very much for the clear explanation with examples. it was very helpful.

@MariosMathTutoring 10 месяцев назад

Glad it was helpful!

@jonahheschel1199 Год назад

Thank you!!! This helped me so much since I missed the start of this unit.

@MariosMathTutoring Год назад

Glad I could help!

@hellohudsons 2 месяца назад

Wonderful videos. I’m studying for my Precalc 2 final, and your videos have been a great help. Thank you!

@MariosMathTutoring 2 месяца назад

Awesome!

@lavenderscent2334 2 года назад

4:44 9:07 11:20

@motoverse-k7z 3 дня назад

Thank you Mario ❤

@johnmicoong8106 3 года назад

Thank you this is very helpful..

@rojanbowl5064 6 месяцев назад

Thank you. God bless you!

@thelight1622 Год назад

Amazing explanation

@irwi_n4078 2 года назад

This guy is honestly goated

@manuelramos6151 2 года назад

OMG thank you so much. Life saver

@hollypoole4333 3 года назад

this was so helpful

@MrBej 4 года назад

Very helpful, thanks!

@MariosMathTutoring 4 года назад

You’re welcome Nayem!

@tolinhnguyen79 Год назад

Thank you very much

@attusiii 3 года назад

I love this human

@ohhesnumb4409 Год назад

Well explained

@user-gp5sr4eg8g 8 месяцев назад

sir you the best no lie

$@frackyoupunk$

@frackyoupunk 2 года назад

Does anyone know how to do these when you have to demonstrate the change in the x and y coordinates? say if the original x value was pi/2, and you had to change the value based on the movement of the graph, how would you go about that? the equation in y=-3sinx-2. I can understand how it happens, but I am having a hard time multiplying and dividing an amount of pi from the original x coordinates.

@habebawael5099 3 года назад

thank you 🙏🏻

@adityasingh1058 2 года назад

amazing video sir

@captainhoops9922 Год назад

thank you very much this was very helpful

@MariosMathTutoring Год назад

Glad it helped

@nnizzel1003 2 года назад

Thank you!!!

@jaimiewallace3127 Год назад

you just saved my life

@rafaelibarra280 9 месяцев назад

Very clear. Thank you

@MariosMathTutoring 9 месяцев назад

Glad it was helpful!

@yinyang9508 8 месяцев назад

He explained in 14 minutes what my professor takes 2 weeks.

@aidanw6725 2 года назад

Thank you

@zoro.mf69 2 года назад

Sir thank you so much

@user-bz2hz7ty1u 4 месяца назад

That was extremely useful

@MariosMathTutoring 4 месяца назад

Glad it helped

@arifhossen7785 3 года назад

From Bangladesh seeing...Thanks

@isabellawilliams52 2 года назад

god bless you mario. I hope your pillow is COLD tonight.

@tont0665 3 года назад

you are the best

@sofiyanoroozi2021 Год назад

You saved me from failing ❤️😁

@thytran271 3 месяца назад

omg u save my life ❤😭

@Soltani88 2 года назад

This saved the day! My teacher did a horrible job teaching this compared to you. Thanks

@hellohudsons 2 месяца назад

Thanks!

@MariosMathTutoring 2 месяца назад

Thanks for the Super Thanks!

@Bitanu07 Год назад

What will be the range of example 7 ?

@kwang-suglee7423 4 года назад

Thank you!

@MariosMathTutoring 4 года назад

You’re welcome Kwang-Sug!

@kaylale2911 3 года назад

@gracepark3188 3 года назад

You are my savior. I bow down hallelujah.

@jamesanterola3680 3 года назад

!!!

@justinels2632 4 года назад

could you graph a more complicated equation, such as, y= -2sin2(x+ pie/6) +1, and the domain be [-pie,pie], i cannot seem to find something like this on the internet, i struggle with identifying the endpoints of this. thank you

@MariosMathTutoring 4 года назад

Justin, this other video I did on graphing trig functions may help you: Graphing Sine, Cosine, Cosecant, Secant, Tangent & Cotangent (Complete Guide) ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE--nr5KCitdGw.html

@ninadee9753 Год назад

11:04 one thing I do not understand about this is the fact that when you plug in 2 for the equation for #6 it doesn't equal 0?

@PaulGovcorrupt 5 месяцев назад

I am a 55 YO, Pre calc student. Lol (Stay teachable)This has really helped understand this topic and these formulas. Thanks

@MariosMathTutoring 5 месяцев назад

Glad it was helpful!

@PaulGovcorrupt 5 месяцев назад

Are you for hire on a 1 on 1 basis ?@@MariosMathTutoring

@sandwich9404 4 года назад

Hey Mario, What math course is this?

@MariosMathTutoring 4 года назад

Hi Tyler...usually Algebra 2 and/or PreCalculus...covered as the trig part of the course.

@ElCruncheroEditz 2 года назад

for number 4 isn't 5pi/4 supposed to be 9pi/4?

@waja6001 2 года назад

Good

@mohamedawale587 Год назад

y = 3sinx -3, i think it streches above x-axis 3 units. maybe i am wrong

@user-cm1jv5xf9w 2 месяца назад

when graphing should i stop at the first period or i should continue?

@MariosMathTutoring 2 месяца назад

Depends on what the instructions state….sometimes it will say graph from -2pi to 2pi or it might say graph 2 full periods, etc

@AbielTesfaye-qn9mt Год назад

THX SO MUCH YOUR SO MUCH BETTER THEN IXL

@MariosMathTutoring Год назад

Thanks! Glad my video helped you!

@Youwishyouknewwhohuh_ 2 года назад

will you always divide the period by four? can you explain more why you divided by four

@RaffaelloLorenzusSayde 2 года назад

We are looking for the period in 1 quadrant in a total of 4 quadrants (horizontally) of a unit circle (portrayed unto a sinusoidal graph), so that would be the equation 1/4 quadrants times the period 2pie/|b|= per 1/4rth of a period. The starting point will be d and thus, we will add by the 1/4rth of a period each time. Btw, every curve is a quadrant.

@abrarkhair5346 8 месяцев назад

You are amzing

@MariosMathTutoring 8 месяцев назад

Glad you like my videos!

@phwataabdul8272 Год назад

are you master Ying C? anyway, your tutorials are best

@jeyakumari 3 года назад

but why are dividing the period by 4 in both sine and cosine graph?

@slovajleclerc9093 3 года назад

Because circle dividend into 4 parts through a full cycle

@RaffaelloLorenzusSayde 2 года назад

@rypto8700 2 месяца назад

i love you

@ninadee9753 Год назад

Why does 2pi/b equal a period? I've thought that is so arbitrary

@Youngballer739 2 года назад

at 11:00 The maximum should be 2, not 1

@mohamedawale587 Год назад

sorry u r right

@Algebrainiac 4 месяца назад

These take so long to graph. They’re very very hard for me…. I’m a math tutor and I make math vids so I haven’t made videos on this. They’re a b*tch to do…!💀💀💀

@suza_627 2 года назад

I am so confused. I'm gonna fail.

@RaffaelloLorenzusSayde 2 года назад

If you're confused about the period. Here is my explanation (hope it helps): We are looking for the period in 1 quadrant in a total of 4 quadrants (horizontally) of a unit circle (portrayed unto a sinusoidal graph), so that would be the equation 1/4 quadrants times the period 2pie/|b|= per 1/4rth of a period. The starting point will be d and thus, we will add by the 1/4rth of a period each time. Btw, every curve is a quadrant.

@may8128 2 года назад

did you fail?

@icebreakmusic2291 3 года назад

what? still searching RU-vid for math help? are the videos from 2006 really helping? yes, yes they are, now get your crappy PowToon lookin animations outta here.