Graphing Trigonometric Functions, Phase Shift, Period, Transformations, Tangent, Cosecant, Cosine 

Hi everyone, I just want to mention a few corrections that you should be aware of. At 33:24, it should be pi/2 and 3pi/2 on the x-axis instead of pi/4 and 3pi/4. At 56:36, it should be 3pi/4 instead of 3pi/2.

This man taught me in an hour what my math teacher failed to teach me in 3 weeks. I love you sir

This guy has singlehandedly gotten an entire generation through math class in schools and colleges of the anglosphere. You put professors and the entire educational system to shame. Thank you.

Don't mind me, these time stamps are for myself (exam is for Range and Domain only). csc(x) : 33:00 sec(x) : 37:40 Acsc(Bx) + D : 41:04 [ Simplified example - 'D' has no effect ] Asec(Bx + C) + D : 45:20 [ Good example - C's effect: 'Bx+C = 0'. x = x0 - P = 2π/B - P + x0 --> Domain ] *sec* cot and - tan : 54:44 [ A's effect ] Acot(Bx + C) + D : 1:00:22 [ Good example - C's effect: 'Bx + C = 0'. x = x0 - P = 2π/B - P + x0 --> Domain ] *cot* Atan(Bx + C) + D : 1:04:47 [ Good example - C's effect: 'Bx + C = π/2'. x = x0 - P = π/B - P + x0 --> Domain ] *tan*

You have helped my Mrs. and I throughout college. Thank you for all that you do.

the way we pay to learn in college just to end up teaching ourselves.

This deserves more views, better than my lectures

1:01:27 Uh, pretend this comment doesn’t exist, I’m just using this to hold my space So how’s your day? Water tastes really good at this time of day, make sure you have a glass every now and then.

I really wish teachers would take a note or two from this guy. He covers all the bases, is very consistent, and explains in detail the reason why every single number has an effect on the graph/function. 10/10 wish he was my teacher.

Be honest your teacher isnt that bad but you werent listening during class

I think it would really help if you put time stamps in the description showing at what time you are going over the specific topic

I seriously rather pay all my tuition for my university math course to him rather than just wasting my time and money over NOTHING at university

(for my own reference) 51:13 basic y = tan(x) graph 57:38 3tan(x) + 1 1:04:02 y = -2tan(x/4 - pi) + 3

Trigonometry Formula Sheet: bit.ly/47diggI Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections

My teacher couldn't teach me this intuitively in a whole month, this guy just taught me in one simple hour

I really like this guy because he does the examples that my teacher doesn’t ever do. I need those examples to learn it and these videos are perfect for that!

phase shift starts at 24:26

switched to online classes and my professor told us to teach ourselves. Thank you for putting in more effort than the man I'm paying for. this lecture helps so much!

i dedicate my newfound interest in maths and physics to you. thank you

You are doing the lords work my friend

personal time stamps 27:15 phase shift 56:29 cot(x) 32:40 csc(x) 37:40 sec(x)

Dude, you taught me 3 lessons worth of my classes. I could barely focus in class or pick up what she was saying. thhanks dude

I watched the entire video. Kind of saved me for my test :)

Brother! In the name of Jesus thank you for allowing me to understand asymptote for tan and cotan; was legit bothered that I was not understanding because I was watching other videos and my teachers videos but still not understanding. You are a true blessing!

You are such a great teacher! I have dyscalculia and am trying like hell to get to abstract math & linear algebra. Thank you so much for so many videos with abundant examples. Your teaching style is what academia lacks; no wonder I can't get through it. You're an inspiration my friend! Keep it up PLEASE!

That was one smooth sine wave at 9:09. All of these videos are making this summer term bearable. Thanks a bunch for them. You have replaced my teacher.

sent from heaven thanks brother from another mom

Wowww very detailed tutorial. Thank you!

For me it helps to think that amplitude, period, phase shift and vertical shift are in alphabetical order so that’s the order they go in. Just dropping this in case it helps someone else!

Wow these examples were much harder than the test. lol Got me an easy 96/100 watching your videos. The extra credit problem i aced was almost identical to your final example of advanced graph equations. cheers!

this gigachad made a 1 hour video for us....

I just watched this whole ass video I hope I pass my test tomorrow, btw it's 12:30am

I'm just gonna start watching ur videos every day

this is soooo fking helpful god it save my life. Hope i will do good on my math quiz tomorrow (u teach better than my math teacher XD)

Thank you for your videos we appreciate it so much. It is crystal clear and you make it enjoyable because you explain very well. You should really be awarded for your well explained videos, whether that is organic chemistry, math or other subjects. Best teacher ever. You should literally teach at a university level courses and I think if you did people would start getting better grades and passing class with confidence. Also, your voice is meant to teach others because it so soft and clear and it isn't intimidating like others. We love all your content, so thank you so much for everything you do and the valuable time you spend on making your videos a high quality content.

You save my GPA. God bless you.

Memo for myself _________________________________________________________________________ [ The relationship: The unit circle (radius = 1) & Trigonometric functions ] The unit circle (radius = 1): --> (x, y) = (cos θ, sin θ) Trigonometric functions y = sin x --> ( The same degree θ from the unit circle, y-coordinate ) Trigonometric functions y = cos x --> ( The same degree θ from the unit circle, x-coordinate ) _________________________________________________________________________ [ Order of drawing sin and cosine functions ] f(x) = Atrig(Bx - C) + D A = amplitude B = needs to find the period p = 2pi/B C = phase shift D = vertical shift (distance from middle line) (1) Draw x-axis & y-axis (2) Check vertical shift to draw middle line of the graph (3) Find a period (p = 2pi/B) to divide to 4 sections on x axis (4) Find upper limit 'D + |A|' & lower limit 'D - |A|' to find range [D - |A|, D + |A|]. The distance from middle line to upper limit = The distance from middle line to lower limit (5) Plot (When there is no phase shift (horizontal shift)) sin The first starting point of sin function is the middle point on the y -axis even though there is a negative sign like y = - sin x. The sin function is about y values of the unit circle. Multiply any (+ or -) numbers of 0 is still 0. And the 0 is from the first point of the unit circle. The 1st spot of unit circle (1, 0) = (x, y) = (cos θ, sin θ). cos The first starting point of cos function is the upper limit or lower limit. When A is positive number --> starts from the upper limit on y-axis. When A is negative number --> starts from the lower limit on y-axis. (x-reflection)

Great vids! Love how they build up and they make sense to me!

I am going to take notes and watch this entire video. Thank you for this gem. :)

Thanks to you I got A in my trigonometry exam. THANK YOU SO MUCH

@ 7:00 mins - "just some things to know" are really crucial.. thanks

Thank you so much Ochem Tutor. Im not sure why Trig is such a hard concept for me to grasp, but you are making it a little easier every video

this shit is just completely and utterly impossible for me. i do everything right, get the correct values for period, key points, amp, vert shift. and i still get the graph wrong. fuck this shit

Professors just get paid to give you a grade and none are going to teach as well as this guy can. You're better off just buying the textbook and supplementing it with this guy's videos.

this is a hard carry on a large chunk of my class you're a legend bro

such a clear and great video. I used this for my precalc test and now I'm using it to review for calc. Thanks!

Why dont you guys do example problems of the type that cause us to struggle the most? like one that includes something like 3pie plus 1/2? notice there is no pie in the 1/2. this is causing me lots of trouble right now but no one seems able to explain how to do this.

So the hour long videos are basically the small 15-20 minute videos rolled into one video?

deadass my prof just had a 5 minute discussion with us today and just sent us this link afterwards 💀

Thank you SO MUCH! You are an amazing math teacher. I am studying for a Calculus exam so I can teach all levels of math in high school (right now I only can teach up to Alg2/trig because I have a credential in foundational level math), and you have been a HUGE help in the studying process. I am so grateful for your explanations and videos!

4:19 Sine and Cosine 32:21 Secant and Cosecant 51:36 Tangent and Cotangent I may be wrong about this, lmao, but just try.

had a D in trigonometry. came across this video that explained it leagues better than my teacher, and I have a quiz on this tomorrow so I hope I do good.

I would actually donate for a face reveal

your voice makes me wanna learn maths- you've done the impossible tysm

Best TEACHER! u helped me out so much, Thnx alot

I am sure most people have already said this. But thank you so much for your help with this. Literally, my professor who has a master's degree could not teach me this, but you could. So thank you again for your help.

Thanks! This video helped me get an 88% on my quiz.

could you recommend me a good book about high school trigonometry , algebra and physics?

currently in Pre-Cal learning this, cuz of home problems i can't focus in school but now i learnt a 2 hour lecture in a little over an hour, thank you

My test is today, and I didn’t understand anything in class. This is my savior

Life saver my god! The entire lecture😭 thank you so much

I have to mentioned this might help me, im just wanted to start looking at stars.../Trig functions are crucial with such things..im like wishing in High school, i was more interested, 20 years later... but i think..you are very good in composing this string...theory. * Cloud Kudos

You are a blessing😭

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I was confident in missing one class because I knew I'd learn it here. Thank you for the thoroughness.

thanks organic chemistry tutor keep it up but better refine your voice quality from next time it seems very unconditional anyway thanks for your math videos better than patrick jmt

51:15 Tangent

Wonderful explanation

I shouldn’t even have to take class if I can just learn it this way.

This guy is the greatest!

This dude singhlehandedly saved me from so many exams. My teacher teaches really badly, so I'm not anxious that I wont understand what we're learning because I know I have you on youtube to teach me. Thank you for what you do, your the best teacher in every subject and you have made me extremely happy. Never stop because we need more people like you in this world. You have been my true mentor in mathematics journey in highchool.

The narrator does an excellent job of explaining the different trigonometric functions and how to graph them. Do not focus on the two minor mistakes. Thank you.

I think the name of the channel is too exclusive to organic chemistry when the videos put up are like everything STEM. Thanks for the vid btw ;)

Hi, I hope you'll excuse my basic question: how can you tell when to use a positive or negative sign in front of the amplitude?

At 36:20, couldn't you have just said x cannot equal n(pi) where n = n/pi? Great job by the way. Studying to this has been a joy

Your videos are extremely helpful. I can't understand why my school doesn't teach me like this. Thank you!!

small error: at 33:35 it is pi/2, pi, 3pi/2, and 2pi. the error was that pi/4 should be a point

God,I hope this man is doing well because I’ve never understood math better in my entire 12 years of schooling

20:51 if cos starts at 1 normally, shouldn't the vertical shift of 2 make the wave start at 3?

Thank you for this video. I you running through examples, i am able to stop the video, solve on my own and then check my answer ensuring mastery of the process. Thank you!

your videos help a lot man thanks idk what id do without you

46:10 sec/csc Atrig(bx+c)+d Timestamp for me

Thank you for your videos we appreciate it so much. It is crystal clear and you make it enjoyable because you explain very well. You should really be awarded for your well explained videos, whether that is organic chemistry, math or other subjects. Best teacher ever. You should literally teach at a university level courses and I think if you did people would start getting better grades and passing class with confidence. Also, your voice is meant to teach others because it so soft and clear and it isn't intimidating like others. We love all your content, so thank you so much for everything you do and the valuable time you spend on making your videos a high quality content.

This is the best video ever. You can't fail a question on trig graphs the video is clear and straight forward

This man just saved my exams! Thanks a lot!

Thanks King. As always, you saved my ass.

I love that you have a video on almost everything.

fucking love u man

Idk what to say tbh u r amazing teacher !!!!!! Iam from syria and I live in Egypt and u help me A LOOOTT thank u really i hope u will read my comment 🔥❤️✨

notes just for my reference (im going to nap lol): SIN AND COS GRAPHS: remember the general shape of the sin and cos graph a - amplitude (distance from midline to max/min point) max - a = midline min + a = midline b - T=2pi/b T - period (distance from one point of the graph to the next point) face shift (where the first cycle of the graph starts): bx+c = 0, x= face shift where one cycle of the graph ends: face shift (x val) + period when graphing, plot the d value first, then the max and min points based on amplitude, the face shift and end, the 4 intervals. TAN GRAPHS tan(x) always has a asymptote of pi/2 and -pi/2. always has (0,0) midpoint/midline is average distance between the last asymptote and its next asymptote. find the next asymptote by adding the period (T = pi/b)

The tutorial is straight forward, it has cleared my confusion.

You are literally so good at what you do- it is so helpful!! Thank you SOOOO much, JG!

How would the equation for a trig function look if it starts like a sin function but never drops below the x axis?

Hi can u do some videos on extended factorials? U don't have to, but It will be helpful for me , thank you in advance.

My life would be very different i guess if I had a lecturer like you

Heyyy sir, I am more interested to learn y=Asian(box+c)+d to determine the equation from graph. So if you had already done can you send me link . Or when you didn't made any video about it then can you make.

You are really amazing in teaching,you have explained this concept in details.I was having difficulties in understanding this but you have helped me a lot.Thank you so much.I enjoyed this

I guess,teaching isn’t your profession but passion.you are the realest and rare one.

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thank you soo much! I was ready to drop my trig class until I tried your video. I was able to understand the formulas with you. With the online lectures, I was lost, confused and discouraged. Thank you!