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

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

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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39 Responses to “Graphing Sine, Cosine, Cosecant, Secant, Tangent & Cotangent (Complete Guide)”

  1. Locky says:

    This man is a god.

  2. Glenda Kiamco says:

    Thank you so much for your very student-friendly videos. May you continue to make more Math lesson-videos. God bless.

  3. Tirth Patel says:

    you just saved me inn my math test bro thanks !

  4. DankMemesMeltSteelBeams says:

    Getting an education in America is paying a college thousands of dollars to explain complex problems and then ending up on YouTube to a free series for a better explanation then what your thousands and every day of being in class is doing.

  5. nameless says:

    thanks helped with my hw

  6. Shivansh Tripathi says:

    Very helpful vedio keep it continues for us thank you so much.
    God bless you!.
    I am from. INDIA🇮🇳

  7. Guelan says:

    That time stamp is a life saver

  8. Mochi Gamble says:

    You’re such a phenomenal teacher Jesus christ

  9. Ghassan Halabi says:

    what a legend. thank u mr mario

  10. كاظم عدنان عطيه says:


  11. romella looc says:

    OMO thank you so much, sir! Now I understand. Your vids was always a big help! I've been watching you all this time and it was fun! Thanks a lot!

  12. Elian R says:

    Thank you so much. Very helpful

  13. walex gaming says:

    lmao this was way easier to understand than my teacher

  14. Rosamelia Carioni says:

    Thank you <3

  15. Abdoulhady Assim Mohammed says:

    I believe THANK YOU won't ever be enough, sir!
    But may ALLAH reward you 💚

  16. Lilli C says:

    you just saved my life

  17. Jake Rader says:

    OMG thank you!!! I’ve been learning how to do this for weeks in my class at school and never got it and you made me understand it in a 30 minute video 40 minutes before my final exam. Thank you this saved me. Keep up the amazing work and maybe give some advice to teachers around the world

  18. Marko Spas says:

    God bless homie

  19. Andrew says:

    you have saved me

  20. Sky_Y says:

    May i ask a question : If the Pi/2 in 1:16 were to be 2 cm ( or two boxes) would the Pi/4 in 3:43 be 1 cm (or one box) ? ( What am trying to ask is does the Pi scale up and down if u were to write it on paper ? ) No right?
    Also it a really good video 😀

  21. asma ameen says:

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

  22. greeshma chowdary says:

    Thanks a lot this helped me a lot and I learned soo much from this my teacher uses to lag this topic nearly 2 to 3 classes thank you

  23. ClaytonLivsey says:

    Damn buddy, don't you need a drink of water?

  24. mar mar says:

    Thanks to you I’m pretty sure I’m going to get a good grade!! Thank you!

  25. Jerry Smith says:

    Thank you Mario. You packaged everything up in a very comprehensive way.

  26. Ashley 333 says:

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

  27. Mohammad Khan says:


  28. Gaming4 All says:

    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.

  29. Massage Asa says:

    Wow this is the man! Made my trig class easy! Thank you. Subscribed be back soon!

  30. nischay rawat says:

    you guyz are great i dont know why you have only 105 k subscriber

  31. Navid Qazizada says:

    Thank you so much for this Mr. Mario

  32. MAD says:

    every person should know this guy's name. he's so gooooooooooood

  33. Alexander Bobrovitskiy says:

    Excellent! Thank you, Mario!

  34. Isaac B says:

    Like all bald characters, this one is overpowered.

  35. Matthew Taylor says:

    Approximately 23:38 (Problem 16) he places the Vertical asymptotes at -pie and +pie. I thought verticle asymptotes can only occur at +pie/2 and -pie/2 because they result in a zero in the denominator? Is it because of the period change?

  36. jorge Samanez says:


  37. Robbie Dosa says:

    Very helpful! Thank you !!

  38. Taggart Jenkins says:

    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.

  39. 5w0 rl1 says:

    Just in at 1:50, you've already made sense of so much. For some reason my college professor SOARS through the lecture and I catch about 65% of what she says. Also, she didn't explain what she meant by "basic sin graph" she just started drawing real fast and said, "as you know you should refer back to this," and I'm like "wha?" Just know you're filling in the gaps for many misunderstandings. Thanks!

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