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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
 one year ago
 one year 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
 one year ago
 one year ago

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wioBest 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?
 one year ago

bii17Best ResponseYou've already chosen the best response.0
Diffrentiation with respect to time.. @wio
 one year ago

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

bii17Best ResponseYou've already chosen the best response.0
\[\sec^2 \theta =8 \cos \theta]
 one year ago

bii17Best ResponseYou've already chosen the best response.0
\[\sec^2 \theta =8 \cos \theta\]
 one year ago

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

wioBest ResponseYou've already chosen the best response.3
Do you still need help solving for \(\theta\)?
 one year ago

wioBest 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?
 one year ago

bii17Best ResponseYou've already chosen the best response.0
what will happen next?? no idea. _
 one year ago

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

bii17Best ResponseYou've already chosen the best response.0
then it will become 1= 8 cos^3 theta ??
 one year ago

wioBest ResponseYou've already chosen the best response.3
Yes! So what about getting rid of the coefficient?
 one year ago

wioBest ResponseYou've already chosen the best response.3
Now it's just algebra. We learned that long ago.
 one year ago

wioBest ResponseYou've already chosen the best response.3
How do you get rid of an exponent?
 one year ago

bii17Best ResponseYou've already chosen the best response.0
hmm i dont know can u help about it?
 one year ago

wioBest ResponseYou've already chosen the best response.3
Why don't you take the cubed root of both sides?
 one year ago

bii17Best ResponseYou've already chosen the best response.0
oww okay I get it :) THanks
 one year ago

wioBest 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.
 one year ago

wioBest ResponseYou've already chosen the best response.3
Otherwise there would be many solutions!
 one year ago

bii17Best ResponseYou've already chosen the best response.0
I get theta = 60 is that correct?
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
Great explanation @wio :)
 one year ago
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