Graphing the Sine & Cosine Functions - [2-21-8]

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Twitter: / jasongibsonmath
In this lesson, we will learn how to graph the sine and cosine functions in trigonometry and precalculus. These two functions are arguably the most important functions in math. We will learn that the sine and cosine functions are projections of the radius of a circle onto the x and y axis. The cosine is the projection onto the x-axis, while the sine is the projection onto the y-axis. Additionally. Any other periodic function can be reconstructed by an infinite sum of sine or cosine functions. This is called Fourier analysis.

[@lyricass7810]

You are true master when it comes maths explanation conceptually.

[@philipjohn1338]

You are a master at teaching. Thank you for posting free videos, they are invaluable to many students.

[@SurenRangaraju]

Hi Mr.Jason - You are such an amazing teacher. As a parent I learn a lot from your videos to teach my kids and broaden my own understanding. This video on sine and cosine is pure gold.
THANK YOU!!!

[@AdityaMishra-gd6vb]

Sir now a days I realy on you to understand these vital topics .
A request please keep making these type of lectures .
You are the best teacher I have seen.

[@pistolpete349]

Your lesson today brings back fond memories of Electrical A/C Theory and many years of learning. Great presentation. Thank you.

[@dammitmom]

literally a life saver ! your style of teaching is amazing and very helpful 2 someone with adhd

[@pinkfrogg]

Incredible lecture. Thank you so much! The most helpful video on TH-cam!!!

[@wilkyclergeot9416]

" The best ever in everything"

[@MathAndScience]

Wow thanks!

[@nisri1567]

Excellent! They way you present you lecture, realy surprising! Thank you for the effort and precious time you are investing to teach the whole world.

[@MathAndScience]

You are very welcome!

[@boonga585]

Just wanted to say thank you for everything tremendously helpful

[@freedomaugustus1555]

i've been waiting for the graph of trig functions.. thank u for that ❤

[@mariocesarsousa]

Indeed it is teacher. Ive just started series and signs with Oppenhein's book and i need to improve my understanding of integrals too. Great and important lesson.✍️✍️✍️✍️

[@letelete3631]

Thank you, I love your lessons❤

[@darkfox77]

Very good video. Very good examples.

[@RamiK101]

Great stuff! Thank you, again. Such a great breakdown.

[@MathAndScience]

Thank you!

[@mewsicman9541]

I've gained an additional knowledge again today! Thanks sir Jason!

[@IsaacHernandez-dr1th]

OMG thank you. I wish you were my math professor.

[@rajant318]

Why graphs of sine fuction do not resemble unit circle? Why these graphs are always bellshaped

[@malihamehjabinnafisa29]

Thanks for your important video.

[@qullin_2238]

I want you to know that the computer demo was brilliant! Btw i know this is unrelated but in the future calculus lessons could you explain in a bit more detail exactly why the derivative can also be written as
"dy/dx" ? For me the fact that they are divided is confusing, i'm sure i'm not the only one!

[@michaelzap8528]

After watching this video i decide to Let my son register your course

[@AugustineJOwamiNthemwe-oq1gu]

You are an awesome lecturer

[@simpleman283]

Good lesson. I'll have to watch the function shift a few times. 35:20

[@johnbond938]

Very helpful thanks very much

[@tresajessygeorge210]

THANK YOU... SIR...!!!

[@Its.namnam813]

Thank you sir

[@thexman5856]

You do a great job 👍

[@MathAndScience]

Thanks so much!

[@sxmmii_gxchaa774]

Thank you

[@ByronKapavolomo]

Best move 😊

[@drumtwo4seven]

Nice 👍

[@abdirasak5597]

Plz why on the table you have shown when added both cosine and sines are not equal to one

[@silentbooks3879]

Awesome

[@hemarajue2736]

I think sin(π/2-x) and sin(x-π/2) represent the same phase shift except changing their sign.

[@sosobara6039]

Non variable reasning please

[@drkrunchy8791]

i love yah

[@jbird4478]

I've seen a lot of videos about this by now, but each and everyone of them just keeps referring to the same basic angles. As if all angles are are either multiples of pi/6 or multiples of pi/4. Arbitrary angles are apparently not a thing, and when someone does mention it, it always boils down to "now let's grab the calculator/computer". Surely these computers do not apply magic, but whatever it is they do when you press sin(x) seems a secret nobody is willing to explain. I highly doubt that in order to graph sin they point to an already existing graph, like this videos does. I don't want to be too negative, but you have numerous videos just explaining the same thing over and over again. Yes, I get it. A circle goes round and round and thus sin keeps repeating. I was hoping at some point you'd get beyond that and explain exactly how the outcome of these functions is calculated - not the basic angles, but for arbitrary input.

[@rithevikaravind815]

First