Graphing Sine, Cosine, Cosecant, Secant, Tangent & Cotangent (Complete Guide)

Learn how to graph Sine, Cosine, Cosecant, Secant, Tangent & Cotangent in this complete guide by Mario's Math Tutoring. We go through how to get the graphs using key points on the unit circle. We also discuss how to find the amplitude, period, phase shift (horizontal shift), vertical shift, asymptotes and more. We go through how to graph and remember the parent functions as well as how to do the transformations on more complicated functions. In all we go through 20 different examples to help you master graphing trigonometric functions.

Jump to Section of the Video:
00:00 Intro
0:33 Example 1 Graph y=sin(x)
1:52 Example 2 Graph y=2sin(x)
2:17 Example 3 Graph y=sin(2x)
3:52 Example 4 Graph y=sin(x+pi)-2
5:56 Example 5 Graph y=cos(x)
6:53 Example 6 Graph y=-cos(x)
7:30 Example 7 Graph y=cos((1/2)x)
8:44 Example 8 Graph y=cos(x-pi/2) +1
10:13 Example 9 Graph y=3sin(1/2)(x-pi)-2
12:10 Example 10 Graph y=2cos(4x+pi)+1
14:07 Example 11 Graph y=2sec(x)
17:23 Example 12 Graph y=3csc(pi/4)(x)
18:31 Example 13 Graph y=4sec(1/4)(x+2pi)-1
20:26 Example 14 Graph y=tan(x)
22:03 Example 15 Graph y= 2tan(x)
22:38 Example 16 Graph y=tan(1/2)(x)
24:01 Example 17 Graph y=tan2(x-pi/8)+1
25:51 Example 18 Graph y=cot(x)
27:19 Example 19 Graph y=3cot((pi/2)(x))
28:40 Example 20 Graph y=-cot(1/4)(x-pi)-1

Related Videos to Help You Succeed!:

Graphing Tangent and Cotangent

Graphing Sine and Cosine

Graphing Secant and Cosecant

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[oscarmunozhernandez]

I missed a day of school and I have been lost for 2 weeks. This video helped me catch up! Thanks!

[felforgedaxe]

Plotting those points the way you did to set up the graph was brilliant.

[gamingall]

Fantastic video. I was struggling a lot with this topic and other channel's videos were helpless to me, but this man seriously knows how to teach! I watched his "graphing sin and cos" video as an introduction, then watched this video to finish the unit. I went from not understanding anything about this topic to, while obviously taking notes, fully understanding everything. Thank you so much, Mario, you really saved me from falling far behind in my class.

[dillpickle]

You are an amazing person. Thank you for saving my grade!

[qvnxash]

thank you for saving my GPA holy shit. Never stop teaching please.

[cowgirlhousesoap]

I was struggling to grasp this concept but you made it make so much more sense. Thank you!

[taggartjenkins]

by far the most helpful explination of math in a short amount of time, my trig professor beats around the bush for an hour and a half, pulling numbers and equations out of no where. thank you so much sir.

[koino]

You explain everything so clearly and show the meaning as to why something is what it is, which is something a lot of teachers don't do. Thank you so much!!!!

[asmaameen]

Your Video should be used in every single Precalculus class in the world. Great video, lots of thanks!

[kvassboy]

Thank you so much for this tutorial. I have my math midterm tomorrow and I have a professor who likes to rush everything. My entire class is confused on every math topic this professor has taught and I have to go to channels like yours to understand the topic.

[azulcorrea-dibar]

The king of math saves the day once again!

[best_savage]

Saved me when learning Pre-Cal thanks so much!!!

[reebie]

Omg I seriously cannot thank you enough Mario--I finally understand now!!! So exciting.

[nomsaphiri]

Your a life saver i struggled with graphing now i have no challenges

[Kristielina]

This YouTubers math intuition is on point! Thank you for this amazing strategy!

[GIO-hsrs]

I asked friends and teachers, and none of them gave an explanation as clear as yours. I'm very thankful, keep up the good work!

[funkymonkey]

Man you have to hand it to Mario, this man is a genius. His teaching skills are immaculate and I can understand everything that he says and does just from the way he articulates himself. Every time I watch one of these videos I always come out of them actually learning something. I highly recommend this guy and keep teaching maths Mario!

[Kiwiiizzz]

This is one of the beat guides on this. I have a test I an hour and now I'm sure to pass and get a good grade on it

[Ben_in_k]

reading from a book is so abstract but you really made sense of it all thanks

[GoahVX]

thanks for your video its really help full keep up with your work