Graphing Sine and Cosine Functions with Transformations (Multiple Examples)

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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[mark]

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 YouTube. 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.

[rodneysteenekamp]

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

[ythwybp]

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

[blackforestdruid]

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.

[DanielA-pgno]

Genuinely saving my grade I love you Mario

[Algebrainiac]

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…!💀💀💀

[coachjeffnac]

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.

[icebreakmusic]

what? still searching YouTube for math help? are the videos from 2006 really helping?

yes, yes they are, now get your crappy PowToon lookin animations outta here.

[niallspotate]

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

[RaffaelloLorenzusSayde]

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.

[jasonwolters]

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

[yinyang]

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

[ddahstan]

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.

[durdonabakhtiyor]

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

[chandra]

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.

[sarafinamcinnis]

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!

[dbuc]

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 YouTube. 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.

[georgeh]

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.

[Op_Hunter]

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

[ElCruncheroEditz]

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