Graphing Trigonometric Functions

We love to graph functions, and now that we know about the trigonometric functions, let's learn to graph those too! These are periodic functions, meaning they spit out the same values over and over and over, with a frequency that depends on the period of the function. This will be easy to understand if we have the unit circle memorized, so make sure you've watched that tutorial too, and then let's do this!

Check out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!

[rocks]

You and Organic Chemistry Tutor were the only persons who let me understand this topic. Thank you so much for making online classes a lot easier. :'>

[Figarland]

It makes sense he teaches Italian, math, physics, chemistry... It's Jesus! Hahah :P

[victoriat.]

learned more from this 12 min video than 2 weeks in class

[RedRahiq]

For who didn't get it:

take " y=Asin(Bx-C)+D "


A: is the amplitude
The distace between the horizontal axis and the max/min of the function.

B: affects the period and the phase shift
To find the period, we take " period=2π/B ".

C: affects the phase shift
The phase shift is "C/B", that's why I wrote that B affects it.

D:affects vertical shift
If positive, it goes up by D. If negative, it goes down by |D|.

Hope it helps.

[barrydavis]

Thank you for this video, sir! My vision for beginning a math video series has "everything" you did here: limited review, error-free content focused to match the title, and scripted conversation. I love the graphing technology and the exit ticket. I watched dozens of videos and got very discouraged before arriving at this one. Awesome job!

[amlanashirbadnayak]

so blessed to learn maths from jesus himself

[subashkandel]

hey man you are doing great keep making such videos. i dont why you get less views. but keep doing this you are really inspiring me and my friends to learn.

[aveinmovil]

Hi! Not getting why we divide by two when finding the phase shift of "y=4sin(2x -2pi/3)"

[harshsinghal]

but we can also plug in complex arguments in trig functions and get all numbers on the complex plane. Are there any ways to visualize complex angles like in sin(2+3i)=9.15-4.169i, how can we visualize angle (2+3i)? or is it just rigorous mathematics?

[MXGIRL]

5:44 how is the period of the function pi, but also 2pi/b which one is it?

[astha_yadav]

Awesome!!
Thank you so much. Clear concise, and includes everything needed.
You're Jesus (and look like him toooo)

[CyberSinke]

1:32 there's an error - instead of y=cos(theta) it should be x=cos(theta). If this wasn't confusing enough, further on in the video, x is used to represent an angle theta...

[SAIROSHAN-libx]

Prof in 8:01 i didnt understand why u divided 2 pi/3 by 2 wouldnt that change the magnitude of the horizontal shift

[Nuggetz]

I'm confused about something in this video. You can see in the 1:05 that the range of trigonometric function are the possible sine values but then when it goes in the 1:16 it says that the range of trigonometric function is -1≤y≤1. How did it change from being all possible sine values to -1≤y≤1? I'm literally confused here?🤔 Can someone explain?

[Adam-cnib]

Professor please i do not understand? This seems very strange of a subject to me. Where can I further observe this?

[oliviamou]

why did u do 2pi-3/2 i don't get that part at all

[karmansingh]

hey I don't know if you are still replying to comments but I have been trying to get ahead of my class in school and do trigonometry in my free time however I cant seem to understand how you got to tan=sin/cos could you please help me thank you

[RadoHudran]

I feel like at 6:25 horizontal shift should have a - in front of it, just like we've seen in the videos before

[sushilthakre]

Not understanding anything ? It's maths . I have failed in maths in my 12 th stdio. lol .

[jerrygarrison]

Why did you divide by two when finding the phase shift? Is it because the horizontal stretch of 2 (the coefficient of x) is causing things to compress? If so, what is the relation between the two? Also, I am referring to 7:58 in the video.