Learning to Graph the Sine Function with Transformations

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👉 Learn how to graph a sine function. To graph a sine function, we first determine the amplitude (the maximum point on the graph), the period (the distance/time for a complete oscillation), the phase shift (the horizontal shift from the parent function), the vertical shift (the vertical shift from the parent function) and the x-scale (the distance between the turns and the x-intercepts). After we have obtained these features, we plot the points on the graph and graph accordingly.
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✅ How to Graph Trigonometric Functions
• How to Graph Trigonome...
✅ How to Graph Tangent | Learn About
• How to Graph Tangent |...
✅ How to Graph Secant | Learn About
• How to Graph Secant | ...
✅ How to Graph Sine and Cosine | Learn About
• How to Graph Sine and ...
✅ How to Graph Trigonometric Functions | Learn About
• How to Graph Trigonome...
✅ How to Graph The Sine Function
• How to Graph The Sine ...
✅ How to Graph The Cosine Function
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✅ How to Graph The Tangent Function
• How to Graph The Tange...
✅ How to Graph The Cotangent Function
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✅ How to Graph Cosecant Function
• How to Graph Cosecant ...
✅ How to Graph The Secant Function
• How to Graph The Secan...
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5 окт 2024

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Комментарии : 75

@claralobsiger4284 3 года назад

It’s sad how an 11 minute video on 2x speed has made me understand this entire lesson whereas my teacher’s almost two weeks of ‘teaching’ this only confused me. Thank you so much 😭

@claralobsiger4284 3 года назад

@Ellis Royce You’re right. I don’t care

@euowol 2 года назад

I'm going to need to write you a "Thank You" letter when I graduate. You're the sole reason I am making through my math courses. Thank you very very much.

@esdths 5 лет назад

Here on Brian's videos because some teachers are absolutely incompetent. Thank God for this man!

@joshbrown8291 5 лет назад

These math videos are awesome because they always fill in the important blanks that my professor never manages to mention.

@cjuneholl 2 года назад

Shouldn't this phase shift have been in the other direction? When I plug in the pi/2 and 3*(Pi/2) for x I get 0 and 2 respectively.

@mohinibarrett3347 2 года назад

That's what I thought too. The phase shift is positive so the zero should be at pi/2

@dylanleisler5327 4 года назад

Thank you for illustrating the influence a period change has on the c. It is an issue I've had multiple times.

@mohineesharma4697 2 года назад

I know this video was posted a long time ago but since this is a big platform and many could be getting the wrong information I was to say I believe you grpahed this wrong @BrianMcLogan this function should start at (pi/2, 0) because sine starts at the sinusoidal axis which is y = 0 for this function. The points should be (/pi/2, -2) (pi/2, 0) (3pi/2 , 2) (5pi/2 , 0) (7pi/2 , -2) to graph this.

@brianmclogan 2 года назад

Can you timestamp what point I made the mistake so I can review and correct?

@mohineesharma4697 2 года назад

@@brianmclogan Yes ofcource, I believe it was 10:25 where you did it.

@mibuuphuong9797 6 месяцев назад

I am truly appreciate you and your teaching method. Your videos are awesome and very easy to understand. Thank you so so so much.

@JeramiaValentine 3 года назад

"actually you know what you're in luck" ... I love how he makes you feel as if you've won something ;p

@mohinibarrett3347 2 года назад

Very helpful video but please check the last step in drawing the graph. You should have put zero on the pi/2

@mehershrishtinigam5449 6 лет назад

the graph's initial period should start at π/2 right? Even in desmos it starts at π/2?

@brianmclogan 6 лет назад

yes the initial period starts at pi/2

@mehershrishtinigam5449 6 лет назад

Ok thanks!

@ijose3070 5 лет назад

The final graph should start from pi/2 going up, I think the phone distract u,

@keshaagrawal8530 Год назад

you explained really well but the graph should start from the origin at pi/2.

@Keepcalmliveon5 4 года назад

I got anxiety when he told one of the students to put their phone down and I haven't been in high school in 6 years lol

@Credalfen Год назад

This is such a great teacher.

@CostelloAidan 5 лет назад

3:15 LOL

@ic9459 3 года назад

Uh oh a test.

@grantlieberman3444 5 лет назад

To find the phase shift couldn’t you also multiply pi/4 by 2 because that’s how much period increased by and if you simplify that you still get pi/2

@depressedoptimist6168 5 лет назад

I appreciate it. You're doing good work.

@hopahop8071 6 лет назад

Professor do you have a video that explains the adding and the subtracting of the Pi fractions ? Because thats what’s confusing me through the whole video.

@jeremeybunion2365 3 года назад

Someone got caught vaping in the bathroom at 3:02

@huyyivong7232 4 года назад

Shouldn't the parent function only have 1 as its amplitude since the 2 amp should be the stretch only for this one right because its 2sin and not just sin? Love your videos. They are a very good review for me. Thank you.

@leenaminnawahda281 5 месяцев назад

Thankyou!!!❤

@hectorordonez1917 2 года назад

Good class teacher and Thank you!!!! But Whole ok But the final grafic seems to me Wrong. Supouse to star Sin grafic in (0, Pi/2) By the grafic you are assuming ×=Pi/2 them Y=2 ( Wrong) If: x=Pi/2 Y= 0 ( Correct )

@kaifox101 3 года назад

thanks helped a lot

@sanjeevnethaji8299 11 месяцев назад

The GOAT💪🐐

@epitaphora 3 года назад

i love this man

@ngchineon1674 6 лет назад

10:54 i think the graph should start from pi/2. Because i get 0 when i sub pi/2 into the sin equation

@brianmclogan 6 лет назад

that is correct! thank you for noticing and posting

@FitHappyAndBlessed 6 лет назад

Great video. Your instruction is very clear. I especially appreciate that you validated Ng Chin Eon's observation. The presentation did not clearly lay out which way to shift. My guess is that you got distracted by the visitor and skipped over the direction. Thanks for clarifying.

@brianmclogan 6 лет назад

You are welcome! Happy to help you out.

@h4ikuz4k53 4 года назад

Why did you divide by 4 to get the x-scale?

@rajpapineni5504 5 лет назад

why is the intercept at π/2 instead of π/4? I'm confused because inside the parenthesis it's (x/2-π/4)

@mayrabreault9006 5 месяцев назад

The graph is shifted pi/2 to the right

@byronscott3360 3 года назад

great teacher helped me heeps

@FailedChadLite 4 года назад

Looks like you shifted it left instead of right

@surajp594 5 лет назад

Thank you sir,👍

@tajbibishamim8085 4 года назад

That green pen is very light, difficult to read close up numbers and symbols.

@vladm.6859 5 лет назад

you sketched the graph wrong. it starts at pi/2 where its value is 0 (not 1) and goes on until 9pi/2 where its value is again 0 not 1.

@DailySimplicity 5 лет назад

yeah I got confused until I realized the graph was wrong

@jaspreetaujla512 3 года назад

Yes, you are correct, I also found the same problem.

@qt4279 6 лет назад

you explained it very well. thanks this video saved me!

@brianmclogan 6 лет назад

you are very welcome Tina.

@iUseTrees 6 лет назад

Thank you so much

@brianmclogan 6 лет назад

you are very welcome!

@maham5893 3 года назад

shouldnt the sine graph start from the midline instead of starting from 2

@jaspreetaujla512 3 года назад

Graph is starting at pi/2 and that’s the zero x intercept but I don’t know why Professor made it maximum point? 😟

@dibong5678 3 года назад

Isn't c the phase shift??

@ClumpypooCP 7 лет назад

Shouldn't the red graph be shifted pi/2 to the right? because it was -pi/2 in the function?

@brianmclogan 7 лет назад

no the x/2 changes that shift

@brianmclogan 7 лет назад

try it on desmos

@ClumpypooCP 7 лет назад

Brian McLogan but if you have (x-pi/2) in the argument of sine/cos, you would translate pi/2 units to the right, right?

@brianmclogan 7 лет назад

if it is (x-pi/2 then yes that is correct, if it is ((x/2)-pi/2) then it is pi to the right. Basically set the argument equal to zero and solve

@ClumpypooCP 7 лет назад

Brian McLogan Oh yeah I see, cool. I actually had my trig graph/equation test today. The only question i got wrong was what are the asymptotes of y=csc3x. such a dumb mistake lol cause that question is really straightforward, i just was going too fast. Most likely gonna get 47/48 on the test. Right now im getting 97% in the class. Do you think that test mark will improve it? I'm really aiming to get 98% or 99% in the class, we got 3 tests + the exam to go...

@luzdc9 4 года назад

the teacher forgot to calculate the end of the period, (which is the period shifted by pi/2) which is 4pi + pi/2 = 9pi/2. So that the period goes from pi/2 to 9pi/2.

@qualquan 6 лет назад

good job explaining effect of 'b' on 'c' but then the screw up of x shift direction pointed by several. also poor contrast of ink on white board and untidy writing. the first point made a lot of amends for the rest, so thank you.

@brianmclogan 6 лет назад

yea could have made the video better but glad you extracted some value