Water Depth Word Problem Modeled with Cosine Sine Function

[@georgesadler7830]

Professor RobBob, thank you for an awesome video/lecture on analyzing the time between high tides and the depth of the water. This is a classic word problem in Trigonometry.

[@vomitingteddy]

I cant believe you covered all that in 17 minutes. This took my teacher a solid week. Thank you :)

[@noejaspeado3236]

my only math teacher in all high school. thanks a lot Mr.

[@profrobbob]

You're welcome...please sub and share this free resource with the head of the math department at your school so ALL the students have access to this FREE help...BAM!!!

[@profrobbob]

[@safwankhan199]

You should teach ib HL math !! You would" bam " the teaching

[@profrobbob]

I just started teaching IB HL Math last year. MAN did I learn A LOT. I was planning to start making a bunch of IB lessons, but after working the solutions in my IB book, next year I get to teach out of another new book and a new Calculus book. So I am doing a lot of homework over the next year. The last ~30 math lessons I posted were from the Vector chapter at the end of the book. I am still improving!

[@MrBeautyindia]

You are good. Even better than my math teacher

[@profrobbob]

THANKS for watching and subbing simranjot dulai ...please share my channel with your friends, class and teacher as an additional study reference:D

[@gonsalvesdenyese]

You need to write a text book Professor.

[@profrobbob]

Thanks for the compliment but then I would never have time to make more videos...:( ...and I just want to keep making videos and growing my channel till I have 1 million subscribers and students like you Denyses...BAM!!!

[@vishwasnagaraju8260]

Please do more of these application stuffs. Loved it !

[@profrobbob]

Thank you for watching. I am glad you liked this lesson so much:) More application problems are always better. I will sneak them in when I can. I am currently trying to expand my Alg 1 playlist and my Calculus playlist between teaching at a high school full time doing 4 different subjects!

[@vishwasnagaraju8260]

ProfRobBob Will look forward Boss! ... You are doing a great job. Keep the same thing going. I feel I should have started learning / loving math earlier, it is soo much FUNNN!!!

[@profrobbob]

Vishwas Nagaraju Does that mean math is more "FUNNN" because I'm the teacher?!...lol Don't forget to share and SUBSCRIBE too:D

[@vishwasnagaraju8260]

ProfRobBob It is about both math and the teacher ... Guess what Boss enjoying math now ... In 83rd PreCalc video. Have planned to finish off PreCalc in another two weeks. Have told my friend to watch all the vids, ya he'll will be ON soon. WOW! Boom ;)

[@profrobbob]

Vishwas Nagaraju WOW!!! You've watch a lot of videos, thanks for choosing Tarrou's Chalk Talk to learn from...You could have been my real classroom student! May I ask where you go to school?...just curious.

[@suhleemshady]

VERY helpful explanation, thank you so much. PS: I would've failed my Alg. 2 test without this....

[@profrobbob]

+Jacob Chamie you're welcome...lets celebrate that with a sub and sharing of this channel with the rest of your class...BAM!!!

[@chriswilliams5291]

Thanks for the video. Can someone let me know if I understand the answer correctly? So the boat can enter the port within 4.573 hours after a high tide had occurred, but after that, it will be unable to port because the tides are too shallow again until the tides reach 4.2 meters again which would be after 7.913 hours after the last high tide and then once again the boat can port until another 4.573 hours after the next high tide occurs which continues to repeat in the same manner that a cosine/sine graph repeats endlessly?

[@johnstillman2935]

I really appreciate you and your great videos really helpful

[@profrobbob]

Thanks for choosing #ProfRobBob to learn from John Stillman

[@ReynaTallano]

Situation In your community, farmers rely on an irrigation system that includes circular water tanks. The water level in these tanks varies in a predictable way due to the filling and draining process. Here are the key parameters: Maximum water level: 6 meters Minimum water level: 2 meters Time for a complete water cycle: 12 hours What about this? How can you solve this?😊

[@andrush00]

at 10.22 you write the vertical shift as -5.. shouldn't it be +5? you write +5 later on

[@heroldhenry4257]

umm.. help!! what happened to "C" when substitute all values into y=a cos b(x-C)+d and why is the vertical shift negative?

[@firebreathingmoonbeam3961]

Thank you so much!!! This was so helpful!

[@profrobbob]

You're welcome...glad I could help! Pleas help us grow by subbing and sharing this free channel with EVERYONE:)

[@johnaronson3304]

Also, the sine function introduced at about 10:43 in the video does not plot. You keep switching between the two ways to use "b" which is very confusing. First, my graphing program simply will not accept the form y= n sin(m)(t-c). I can get y=1.2 sin(12.5/8 - 0,503 t)+5 to plot as you say it should but that was only by trial an error.

[@amanchaudhari4115]

I got confused.... you stated in the writing that the boat can go through at those times, however while talking u said the boat can't. BAM!!!

[@profrobbob]

Sorry about mis-speaking. The written summary describing how the boat can enter the port as long as you are within 4 hours and 32 minutes of high tide is correct:) Thank you for watching!

[@yei62115]

Really like your explanation. Could you please make a video to explain "simple harmonic motion" with the same cosine function. Thanks!!

[@johnaronson3304]

This got terribly muddy when explaining how to pick up the second angle after 2.3. There was a lot of arm waiving but I didn't really see why Pi -2.3 = 0.842. I assume you are saying that the second angle is in Q III and the second angle is found by finding the difference between PI and the x axis in Q II (Pi - 2.3 = 0.842) and then adding that to Pi to find the reference angle in QIII. Pi + 0.842.

[@teenwriterii3671]

Very helpful, thank you!

[@profrobbob]

Teen Writer II and THANK YOU for choosing, liking, learning and subbing!

[@kotosqoposrly]

I didn't understand quite well the last part. How is that you got 2.3 and .84?

[@profrobbob]

The calculator gave me 2.3 from the arccos(-.667). The reference angle is 3.14-2.3. Now add that reference angle to 3.14 to find the angle in quadrant 3 where cosine is also negative.

[@mohammadfadayi3818]

hi Mr True, I am really crazy about your teaching do you have any website that incorporated by ample samples of examples?????????????? againg thanks alot

[@adamsichel1903]

If one is doing this problem without a calculator could .503 for b be interpreted as π/6.25 or is that wrong.

[@profrobbob]

+Adam Sichel Fractions should not be written with decimals in them. You can write it as 20pi/125 and then 4pi/25. Thank you for choosing my lessons to learn from:)

[@huihui666]

Wow! This video was sooo helpful! I have a question though. If no time was given and all you are asked is to find a trig function for a problem, then how do u know if to use sine or cosine? And where to start the graph at?

[@profrobbob]

Sine are Cosine have exactly the same shape so you can use either function. I think it is a little easier to set up Cosine because it starts at its maximum value when x=0. Because of this, some students find it easier to figure out the appropriate phase shift.

[@heroldhenry4257]

WOW Tachibana Kanade from angel beats!

[@darkerknight38]

I plugged in cos^-1(-.667) into my calculator and it gave me 131.84. So how did you get 2.3?

[@profrobbob]

I am doing my calculations in radians and not degrees:)

[@leananektalova3000]

For the cosine function, you first wrote y= 1.2cos(.503x)-5, but then when you rewrote it you put +5 instead. I am a little confused, so which one is it supposed to be? And why?

[@architgupta4433]

ur stupid

[@moski9861]

@@architgupta4433 shut up gupta

[@akalis13]

Can you help me with this Ferris Wheel problem? Its confusing because it down not start time until some point that is not the lowest point... *The ferris wheel you are going to ride is 36 feet in diameter. The bottom of the wheel is 4 feet off the ground. The ferris wheel travels at a rate of 3 revolutions per minute. You start the ride at the bottom of the ferris wheel, but do not begin timing then. You start a stop watch while you are riding sometime after you start. After 8.5 seconds you are at the maximum height of the ride. Find two equations, one in terms of cos and one in terms of sin - that will tell how high above the ground you are at t seconds. The value for parameter A must be positive in both equations. Please help!

[@profrobbob]

Your amplitude is 18 and since the period is 20 seconds for a revolution b=pi/10 and the vertical shift is (4+40)/2. So far for Cos we have 18cos(pi/10)x +22. Now to match t=0 is some random time with reaching max in 8.5 seconds move the graph right 8.5 units since cosine starts at its maximum value. I will leave to you to figure out the proper phase shift for sine.

[@vishwasnagaraju8260]

ProfRobBob Shifting the cos curve left side so that origin will have the max value. t=18cos(pi/10)(-8.5)+22=5.9618 For the sine curve 18sin((pi/10)x+(pi2))+22 Hope am correct boss ProfRobBob ...

[@davidnwafor7023]

Vishwas Nagaraju ProfRobBob Will the phase shit for sine be 18sin(pi/10(x+pi/40))+22 ?

[@vishwasnagaraju8260]

david nwafor Sorry ?

[@jessemeng8249]

This may sound stupid, but I don't get how cos-1(0.667)= 2.3, I got 0.84

[@profrobbob]

jesse meng You found a sign error. I miscopied my notes. It should have been cos^-1( -.667). Thanks for watching and doing the problems. Sorry for the small copy error.

[@profrobbob]

jesse meng You are welcome:) Thanks for allowing me to help.

[@demiilovato293]

jesse meng

[@heroldhenry4257]

heh? why is my X=262.04 is this 262.04 in minutes? which is =4 hours and 36mins?

[@brando820]

you look like Mr. Bean

[@andoan4510]

i hate wix, one of the most annoying ad. i will never use it....

[@profrobbob]

I don't have any control on the ads that run but watching them does help support all youtube creators...thanks for watching!

[@andoan4510]

The only problem i have with it is that it pop up in almost every video i watch. I even reported the ad that i dont want to see it and it still pop up.... aye