Graphs of Sine, Cosine and Tangent Functions

This lesson shows examples of graphing transformed y = sinx and y = cosx graphs (including changes in period, amplitude, and both vertical & horizontal translations). There is also an example of how to graph y = tanx using the y = sinx and y = cosx functions. This lesson was created for the MHF4U Advanced Functions course in the province of Ontario, Canada.

[vanillaclouds]

Thank you, this is the first time I finally understood the sin, cos and tan graph even after my secondary school education.. :')

[s-dilettante]

most helpful video I've seen on this topic yet. Thank you, sir!

[joan-sayahdixon]

I have been working on these for days !! was able to do it but slowly. Now i understand better :) Pretty much saved my life.

[AlRichards]

You start with the basic sin or cos graph and use the transformations as per the examples on the video. But always start from the normal y = sinx or y = cosx function.

[AlRichards]

The graph of y = tanx is pi or 180 degrees. It works the same way with transformations as y = sinx or y = cosx. For example, for y = tan[3(x - pi/4)] the period would be pi/3 and it would be translated pi/4 to the right (this part is what affects the vertical asymptotoes). So, we'd draw vertical asymptotoes at pi/2 - pi/4 = pi/4 and then every pi/3 after that since pi/3 is the period.

[AlRichards]

The third graph is shifted to the right pi/6. In the brackets notice the x - pi/6, that means there's been a horizontal translation of pi/6 to the right. So instead of starting at 0, you start the cycle pi/6 to the right.
A good scale on the x axis depends on what the horizontal translation is (and the period). To use pi/2 might not always be convenient. Look at what the period is and what the horizontal translation is to determine a good scale.

[markmendoza]

You taught me more than what my professor goes through hours of lecturing!

[beefcow]

Thanks, this video is gonna save me from failing pre-calc!

[AlRichards]

Hi,
Thanks for the comment. Unfortunately, I don't have an inverse for the trig functions video. However, I do have one for graphing the reciprocal functions.

[AlRichards]

@gsfreako To determine the period from a graph (with no equation) look to see how long one cycle is - that's the period. All you really need to know is the general shape for any particular trig function.

[AlRichards]

Thanks for the comment. I appreciate hearing from people that find my videos useful.

[AlRichards]

The period of 3sin2x is TT and it was graphed from 0 to 4TT, so that would be 4 cycles.

[SuperKA]

how come in the first two graphs you had x intercepts of pi over 2 or 90 degrees, like the first x intercept was pi over 2, then pi, then 3pi over 2. But in the third graph you started with pi over 6 as your first x intercept. I get confused on what I can put as my x intercepts. Should I always start with incriments of pi over 2?

[nicolesaed]

I love your teaching method and I would like to know if you have a video about graphing their inverse...

[rmicrods]

I just realised this is not 3U after seeing tan waves. I can't seem to find any 3U lessons for sine & cosine waves sir. Could you please point me in the right direction, or put up a couple of lessons when ever you can. That would be great review prior to our final exam.

[WhatsGoodxD]

Beyond fantastic! Thank you very much!

[yololzmartinez]

thank you so much, really helpful ! 👍🏻

[AGNajor]

how do u know what the numbers on the x-axis are supposed to be?

[marziaahmadi]

thank you sir it was very useful bat a little clean i inhabit afs but i love this kind of videos

[gsfreako]

how would you determine the period if you don't have an equation ?