Sinusoidal Function Word Problems: Ferris Wheels and Temperature

[@madmaths7895]

What other topics do you want me to cover? Check out the channel for more tutorials!

[@bobk3881]

you don't know me. But I want to give you a hug. I understand it. Thank you so much. I love that you explain why everything on your graph is labelled how it is. Thank you

[@petercote6694]

You don't even know how good this explanation was. I've been struggling with this and suddenly it feels easy.

[@madmaths7895]

Happy to help.

[@Cinnammonroll123]

One of the best Ferris Wheel Problem explanation I’ve seen

[@lulabyee7856]

a lot better than my teacher amazing amazing job

[@anushkabist1170]

You are a lifesaver, thank you SO MUCH.

[@stephaniek3466]

thank you so much dude 🙏🏾🙏🏾 i’m taking honors pre calc next year hope u help out some more

[@coolstar3971]

a fabulous explanation with proper application, thank you.

[@richardbailey2001]

How did you get inverse of Cos ( 4 / 30 ) with an answer of 97.66 ... when I put that into my calculator .. inverse of Cos ( 4 / 30 ) .. I got 82 . 3377 .. where am I going wrong ?

[@madmaths7895]

It is because you are taking the cos inverse of negative 4/30. I forgot to write the negative in the next line. My bad. But the answer remains 97.66.

[@yakshsoni6617]

When do you figure out if there is a phase shift or not?

[@Jacob-of9wf]

thank you for this

[@ElizavetaAleksandraPetrovna]

I have a question for you MadMath, If you have a h(t) graph and your hight as you mentioned is changing faster and faster then it changes slower and slower to a position momentarily at the Max and Min point when the hight does not change , on your hight vs time graph , then isn't it exactly the definition of changing your speed? You say that the speed does not change!

[@madmaths7895]

The vertical speed is changing, yes. (As is your horizontal speed.) The speed the wheel is rotating is not changing though. Basically, your height off the ground might change a different amount in a 1 second period vs another 1 second period, not because of the speed of the wheel, but because of your location on the wheel at that time. This might be tricky to imagine but I tried my best to explain it in the video.

[@ElizavetaAleksandraPetrovna]

@@madmaths7895 Thank you for clarifying what you meant. But of course the speed of the wheel is not changing. It rotates once every 100 second. However the speed of a person in a cart rotating is continually changing. No?

[@madmaths7895]

@@ElizavetaAleksandraPetrovna The person's speed vertically changes, yes. (It may be more appropriate to refer to this as their velocity.) But their speed does not change, no. They travel around the center of the wheel in a circular path at a constant speed.

[@ElizavetaAleksandraPetrovna]

@@madmaths7895 I see. Thank you. I will take physics next year. I know a bit now but I think that's where I lack knowledge. I understand that the speed is constant but the velocity is changing because the path isn't straight and the direction is continually changing. I must dig deeper to understand when I can say from the given information if I can have constant speed while I have acceleration? What you are saying about constant speed make sense so I am missing something. Many thanks for further explanation.

[@RigorousMathematicsByProfUsman]

Is it assumed that the wheel is moving with a constant speed?

[@madmaths7895]

Yes it is.

[@SimonSuhGaming]

ty!

[@BobThef]

thanks very underrated! also on an exam u would likely be allowed to use a calc for finding height and specific time? right?

[@madmaths7895]

Yes, usually you just use a calculator.

[@davidbarker5823]

why would 360/period work instead of 2pi/period ? i thought you had to do it in radians?

[@madmaths7895]

It depends on which units you decide to use. If you are using radians then use 2pi. If you are using degrees then use 360.

[@sjdanial5524]

when i put it into desmos it doesnt make any sense at all. is there a correct way to input it? i am struggling.

[@chloejackson481]

ME RN

[@sarsora5719]

Very helpful!❤

[@lil_uji_goated]

aren't you supposed to use 2pi instead of 360

[@rr.richie]

thats what i thought

[@VadikMironoff]

pi = 180, 2pi = 360 degrees. They're interchangable.

[@JonBonStomp]

2pi is in radians, 360 is in degrees. He's currently using degrees.

[@yksid_1226]

How did u get 36 as the vertical shift, wouldn’t it be 6 since that’s the initial starting point ?

[@madmaths7895]

The vertical shift is the distance from the axis (or midline) to the x-axis. Not from the lowest point.

[@shrimp7127]

what about finding time of when you reach a specific height for 4,5,6th time for example?

[@ellenli3873]

The video shows that

[@salmanel-farsi3744]

The question did specify to use a sinusoidal function, so does not that imply using a transformation of h - sin(t)?

[@madmaths7895]

Sinusoidal functions refer to both sine and cosine functions!

[@marwahaidari693]

We would be happier if you could have written the second question completely with the parts. Thank you

[@HamishaBadhan]

where did he get the 40 from when he was doing the feriis wheel last question

[@madmaths7895]

I was just showing that you could be asked a follow-up question like "when is the height 40ft?" 40 would be given to you in the question.

[@ayellowplum]

Thanks

[@DesziOLeary-Pippo]

How could you explain how to solve the first time equation

[@DesziOLeary-Pippo]

With no calculator

[@madmaths7895]

That would require a calculator for most people, myself included.