Graphing Sine and Cosine with Phase (Horizontal) Shifts, Example 1

[zxrtt]

The only vid about phase changes on Youtube that i actually understood.

Thanks again pat

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[kasidyreynolds]

Thank you!!! :) This is a very well done video that helped me ace my final. Thanks so much!! :)

[xhaliteelza]

Trigonometry is just a phase you go through before you shift to calculus.

[lexinaut]

This is nicely presented, even though it's just a phase you are going through.

[mlemck]

What if your equation is -(1/2)sin((1/3)x+(pi/2))?? We get really complicated equations with pi and we cannot factor out anything which makes if really confusing! can you please help!!!!
- Precalc honors student in dire need of your assistance

[SaiMako]

Seriously tho, thanks a lot Patrick!

I'm currently in 3rd year college studying in a University and a friend of mine asked for helped and I know we took this already before and I forgot it already. I searched your channel and you gave me the clearest explanation!

Keep it up! :)

[glasssmirror]

To make life easier just set the equation to zero eg x-4=0 x=4 then always positive goes to the right.

[EurodancerxXx]

yeah! finally understand how to do a part of my final now!

[patheticness]

Please explain why b) wouldn't be 1/2???

[SuperNation]

@wannabeeish why would you factor it? it has nothing to do with factoring, when you need to make a sine graph to a cos graph you only change the phase shift according to your graph, the equation you give says 3 degrees right therefore, y=2sin4x+3 should be your cos graph

[venusclay]

First I want to say thank you because I've learned so much.  My question is on how to graph sine and cosine functions on the following problem.  y = -2sin 4(x-pi/2) - 1.  I don't understand the steps to take to co this problem.  If you could let me know I would really appreciate it.  Thank You

[alexburrows]

I think achieved is a better word, not received.

[hinatababe]

Funny how you said to "factor out the ten and leave it completely outside the parenthesis is wrong" when I saw this other guy here on YouTube do it! Lol too funny . And thanks for the help 😂✊🏽

[mateeah]

i luvs u patrick. whenever i see a math video and from your name i say YAY PATRICK

[wannabeeish]

you can factor it out of the bracket and put it after, either sine or cosine
as in y=2 sin4(x-3) +3

[xhbkx]

You are so helpful thanks to you i received a 97% on my test

[snakedron]

wat dod u do if a phase shift is in degrees?wat do you do to the graph can someone please help?

[Supermario]

This version of phase shift is very easy to understand, but I have seen versions of phase shift that define the horizontal translation as a fraction of a cycle. Can anyone explain the difference between these two definitions?

[maykiahang]

Ugh I ❤️ you ! I understand math omg .!

[ericagershom]

Thank you so much! This was really helpful :)