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bii17
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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
 2 years ago
bii17 Group Title
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
 2 years ago

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wio Group TitleBest ResponseYou've already chosen the best response.3
Would 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?
 2 years ago

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

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

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

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

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

bii17 Group TitleBest ResponseYou've already chosen the best response.0
i know is sec = 1/ cos
 2 years ago

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

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

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

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

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

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

bii17 Group TitleBest ResponseYou've already chosen the best response.0
1/8 = cos ^3 theta ??
 2 years ago

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

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

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

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

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

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

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

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

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