Graphing Sine and Cosine Functions with Transformations (Multiple Examples)

Рет қаралды 255,446

4 жыл бұрын

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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Пікірлер: 128

@mark8877 3 жыл бұрын

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 KZfaq. 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 жыл бұрын

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 жыл бұрын

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 Жыл бұрын

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

@lukebowman9260 Жыл бұрын

@@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 ай бұрын

Are you sure😅

@blackforestdruid Жыл бұрын

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 Жыл бұрын

Awesome! Glad my video helped you!

@DanielA-pg2no 4 жыл бұрын

Genuinely saving my grade I love you Mario

@MariosMathTutoring 4 жыл бұрын

Glad my video helped you Daniel!

@niallspotat0e823 3 жыл бұрын

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

@coachjeffnac 3 жыл бұрын

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.

@sarafinamcinnis9990 2 жыл бұрын

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!

@chandra68 3 жыл бұрын

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.

@ddahstan6876 2 жыл бұрын

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.

@rodneysteenekamp8924 3 жыл бұрын

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

@ahmadjamal2320 2 жыл бұрын

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

@andrehardaman9375 3 жыл бұрын

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.

@bluecat7431 2 жыл бұрын

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

@durdonabakhtiyor2534 2 жыл бұрын

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 KZfaq channel but yours is one of the best which I have ever seen 👍👍👍👍

@jakahifreeman6614 3 жыл бұрын

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

@jasonwolters7306 2 жыл бұрын

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

@theman7050 2 жыл бұрын

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

@rkumaresh 3 жыл бұрын

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

@georgeh1352 Ай бұрын

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 Ай бұрын

You’re welcome!

@soybean_TM Жыл бұрын

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

@MrBeafyYT 3 жыл бұрын

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

@yojacq 2 жыл бұрын

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

@johnmicoong8106 3 жыл бұрын

Thank you this is very helpful..

@ryanlorenti469 3 жыл бұрын

you’re an amazing teacher bro stg

@arslanmoghal5472 Жыл бұрын

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

@Op_Hunter5 6 ай бұрын

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

@MariosMathTutoring 6 ай бұрын

Glad you like them!

@motoverse-k7z 27 күн бұрын

Thank you Mario ❤

@metookwok6545 2 ай бұрын

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

@sweethmv Ай бұрын

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 Ай бұрын

You're very welcome!

@rojanbowl5064 7 ай бұрын

Thank you. God bless you!

@yasmineyasmine8059 2 жыл бұрын

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

@hollypoole4333 3 жыл бұрын

this was so helpful

@thelight1622 2 жыл бұрын

Amazing explanation

@learnwithjustintoday Жыл бұрын

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

@curtpiazza1688 3 жыл бұрын

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

@habebawael5099 3 жыл бұрын

thank you 🙏🏻

@MrBej 4 жыл бұрын

Very helpful, thanks!

@MariosMathTutoring 4 жыл бұрын

You’re welcome Nayem!

@tolinhnguyen79 Жыл бұрын

Thank you very much

@gutierrezjeffryv.7649 7 ай бұрын

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

@MariosMathTutoring 7 ай бұрын

Thanks! 😃

@manuelramos6151 2 жыл бұрын

OMG thank you so much. Life saver

@RaffaelloLorenzusSayde 2 жыл бұрын

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.

@ferozdba 11 ай бұрын

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

@MariosMathTutoring 11 ай бұрын

Glad it was helpful!

@nnizzel1003 2 жыл бұрын

Thank you!!!

@ohhesnumb4409 Жыл бұрын

Well explained

@jonahheschel1199 Жыл бұрын

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

@MariosMathTutoring Жыл бұрын

Glad I could help!

@user-yt6hw2yb7p 2 жыл бұрын

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

@adityasingh1058 2 жыл бұрын

amazing video sir

@attusiii 3 жыл бұрын

I love this human

@zoro.mf69 2 жыл бұрын

Sir thank you so much

@lavenderscent2334 2 жыл бұрын

4:44 9:07 11:20

@hellohudsons 2 ай бұрын

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

@MariosMathTutoring 2 ай бұрын

Awesome!

@aidanw6725 2 жыл бұрын

Thank you

@user-gp5sr4eg8g 9 ай бұрын

sir you the best no lie

@irwi_n4078 2 жыл бұрын

This guy is honestly goated

$@frackyoupunk$

@frackyoupunk 2 жыл бұрын

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.

@captainhoops9922 Жыл бұрын

thank you very much this was very helpful

@MariosMathTutoring Жыл бұрын

Glad it helped

@rafaelibarra280 10 ай бұрын

Very clear. Thank you

@MariosMathTutoring 10 ай бұрын

Glad it was helpful!

@tont0665 3 жыл бұрын

you are the best

@jaimiewallace3127 Жыл бұрын

you just saved my life

@arifhossen7785 3 жыл бұрын

From Bangladesh seeing...Thanks

@user-bz2hz7ty1u 4 ай бұрын

That was extremely useful

@MariosMathTutoring 4 ай бұрын

Glad it helped

@hellohudsons 2 ай бұрын

Thanks!

@MariosMathTutoring 2 ай бұрын

Thanks for the Super Thanks!

@thytran271 4 ай бұрын

omg u save my life ❤😭

@kwang-suglee7423 4 жыл бұрын

Thank you!

@MariosMathTutoring 4 жыл бұрын

You’re welcome Kwang-Sug!

@kaylale2911 3 жыл бұрын

@Bitanu07 Жыл бұрын

What will be the range of example 7 ?

@isabellawilliams52 2 жыл бұрын

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

@ElCruncheroEditz 2 жыл бұрын

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

@sofiyanoroozi2021 Жыл бұрын

You saved me from failing ❤️😁

@waja6001 2 жыл бұрын

Good

@justinels2632 4 жыл бұрын

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 жыл бұрын

Justin, this other video I did on graphing trig functions may help you: Graphing Sine, Cosine, Cosecant, Secant, Tangent & Cotangent (Complete Guide) kzfaq.info/get/bejne/Y9SiaK50ztrId6s.html

@Soltani88 2 жыл бұрын

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

@ninadee9753 Жыл бұрын

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?

@yinyang9508 9 ай бұрын

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

@sandwich9404 4 жыл бұрын

Hey Mario, What math course is this?

@MariosMathTutoring 4 жыл бұрын

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

@abrarkhair5346 9 ай бұрын

You are amzing

@MariosMathTutoring 9 ай бұрын

Glad you like my videos!

@mohamedawale587 Жыл бұрын

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

@user-cm1jv5xf9w 3 ай бұрын

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

@MariosMathTutoring 3 ай бұрын

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

@PaulGovcorrupt 6 ай бұрын

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

@MariosMathTutoring 6 ай бұрын

Glad it was helpful!

@PaulGovcorrupt 6 ай бұрын

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

@Youwishyouknewwhohuh_ 2 жыл бұрын

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

@RaffaelloLorenzusSayde 2 жыл бұрын

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.

@AbielTesfaye-qn9mt Жыл бұрын

THX SO MUCH YOUR SO MUCH BETTER THEN IXL

@MariosMathTutoring Жыл бұрын

Thanks! Glad my video helped you!

@phwataabdul8272 Жыл бұрын

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

@jeyakumari 3 жыл бұрын

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

@slovajleclerc9093 3 жыл бұрын

Because circle dividend into 4 parts through a full cycle

@RaffaelloLorenzusSayde 2 жыл бұрын

@gracepark3188 3 жыл бұрын

You are my savior. I bow down hallelujah.

@jamesanterola3680 3 жыл бұрын

!!!

@rypto8700 2 ай бұрын

i love you

@ninadee9753 Жыл бұрын

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

@Youngballer739 2 жыл бұрын

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

@mohamedawale587 Жыл бұрын

sorry u r right

@suza_627 2 жыл бұрын

I am so confused. I'm gonna fail.

@RaffaelloLorenzusSayde 2 жыл бұрын

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 жыл бұрын

did you fail?

@Algebrainiac 5 ай бұрын

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…!💀💀💀

@icebreakmusic2291 3 жыл бұрын

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