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 2 years ago
If an angle theta increases uniformly, find the smallest positive value of theta for which tan theta increases 8 times as fast as sin theta
 2 years ago
If an angle theta increases uniformly, find the smallest positive value of theta for which tan theta increases 8 times as fast as sin theta

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wio
 2 years ago
Best ResponseYou've already chosen the best response.3Would it be something like this? \[\Large \frac{d}{d\theta}tan(\theta) =8\cdot \frac{d}{d\theta}sin(\theta) \] Where \[\Large \frac{d}{d\theta}tan(\theta) > 0\] What is the topic of the curriculum?

bii17
 2 years ago
Best ResponseYou've already chosen the best response.0Diffrentiation with respect to time.. @wio

wio
 2 years ago
Best ResponseYou've already chosen the best response.3So do you think you can find those derivatives, and then solve for \(\theta\)?

bii17
 2 years ago
Best ResponseYou've already chosen the best response.0\[\sec^2 \theta =8 \cos \theta]

bii17
 2 years ago
Best ResponseYou've already chosen the best response.0\[\sec^2 \theta =8 \cos \theta\]

wio
 2 years ago
Best ResponseYou've already chosen the best response.3Now, what is \(\sec^2(\theta )\) in terms of \(\sin(\theta) \) and \(\cos(\theta)\)?

wio
 2 years ago
Best ResponseYou've already chosen the best response.3Do you still need help solving for \(\theta\)?

wio
 2 years ago
Best ResponseYou've already chosen the best response.3Ok so we have \[\Large \frac{1}{\cos^2(\theta)} = 8\cdot \cos(\theta)\]How can we isolate \(\theta \) further?

bii17
 2 years ago
Best ResponseYou've already chosen the best response.0what will happen next?? no idea. _

wio
 2 years ago
Best ResponseYou've already chosen the best response.3How about we multiply both sides by \(\cos^2(\theta)\)? Try that.

bii17
 2 years ago
Best ResponseYou've already chosen the best response.0then it will become 1= 8 cos^3 theta ??

wio
 2 years ago
Best ResponseYou've already chosen the best response.3Yes! So what about getting rid of the coefficient?

wio
 2 years ago
Best ResponseYou've already chosen the best response.3Now it's just algebra. We learned that long ago.

wio
 2 years ago
Best ResponseYou've already chosen the best response.3How do you get rid of an exponent?

bii17
 2 years ago
Best ResponseYou've already chosen the best response.0hmm i dont know can u help about it?

wio
 2 years ago
Best ResponseYou've already chosen the best response.3Why don't you take the cubed root of both sides?

bii17
 2 years ago
Best ResponseYou've already chosen the best response.0oww okay I get it :) THanks

wio
 2 years ago
Best ResponseYou've already chosen the best response.3Just remember that you want the smallest positive \(\theta \), and that \(\cos(\theta)\) must also be positive since they should be increasing.

wio
 2 years ago
Best ResponseYou've already chosen the best response.3Otherwise there would be many solutions!

bii17
 2 years ago
Best ResponseYou've already chosen the best response.0I get theta = 60 is that correct?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.0Great explanation @wio :)
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