Calculus 1 - Derivatives and Related Rates (7 of 24) Changing Angle

In this video I will calculated the d(theta)/dt=? at a given point of a person (y=10m) walking away from that given point.

Next video in this series can be seen at:

[ojfotboll]

I would pay so much money for you to be my teacher at my school.... please do more videos on inequalities problems and equations

[ptyptypty]

well done Michel !!... it's nice to see the final This problem was solved for an angle = 30 degrees.. but I can insert any angle now, like 45 degrees, and find the d(theta) due to the final result.... Thanks!!

[ptyptypty]

ah HA.. I read the comments to see if anyone had suggested that you could take the Derivative of TAN and get SEC^2 and then solve.. and it works! :) I see my earlier comment is from SIX YEARS AGO.. omg!! where does the time go.. ??

[wsar]

You could also use the derivative short cut for Tan = Sec^2

[WladyslawAntonsiewicz]

this example is good for a practice. I was going by a different approach but I was like "wait a minute" something is off here, because the angle can't be 30 degrees (100+25)^0.5 = 11.18 so x had to be 5.59 so the Sin(theta) = 5.59/11.18 = 0.5 or the angle 26.565 degrees ... however thanks for the example)❤

[johnnolen]

Professor van Biezen, I solved your problem by implicitly differentiating the Arctan (x/y), and got a different result from yours. The reason is because the distance x in your diagram is mislabeled. For 𝛉 = 30°, tan 𝛉 = 1/sqrt (3), not 5/10 as your sketch suggests.

[pipertripp]

An easier way is to simply treat y as a constant rather than an independent variable so the relationship become one between x and theta:

tan(theta) = x/10

Then the rest goes basically like you've show here. Is there any problem with going this route?

[dalevillarin]

Hello Sir, is it okay to used the derivative of arctan in finding the change of theta in respect to t even without using the 30 degrees angle? If so, what is the difference between your process and using the arctan derivative? Thank you very much for your lectures!!

[jacksparrowization]

hi professor, thanks so much for the videos im learning so much, i tried using Pythagoras theorem on the triangle, and then differentiating but im getting a different answer.. x^2+y^2=z^2, z=10/cosθ, so x^2+y^2=100/cos^2(θ), now i differentiate and then i get a different answer from whats shown in the video..i know that your method is simple, but its just bugging me, not knowing what went wrong with what i did...i always appreciate your replies...thank you so much :)

[MasayoMusic]

I'm confused as to why the answer is in radians. We started with degrees right? Thank you.

[theusualsuspect]

shouldnt the answer be in degree per second as the given angle is in degrees

[ahmedal-ebrashy]

Hello Sir! Isn't y a constant? Then why was it difrentiated?

[r.m]

but actually y is the the hypothesis because 10*sin30=5