## 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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This man is a god.

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

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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.

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10:58

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!

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OMG thank you!!! Iâ€™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

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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?

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THANK YOU SO MUCH!!!!!YOU SAVED ME FROM FAILING

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.

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Excellent! Thank you, Mario!

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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?

exellent!

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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.

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!