anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
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?
anonymous
  • anonymous
Diffrentiation with respect to time.. @wio
anonymous
  • anonymous
So do you think you can find those derivatives, and then solve for \(\theta\)?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
\[\sec^2 \theta =8 \cos \theta]
anonymous
  • anonymous
\[\sec^2 \theta =8 \cos \theta\]
anonymous
  • anonymous
Now, what is \(\sec^2(\theta )\) in terms of \(\sin(\theta) \) and \(\cos(\theta)\)?
anonymous
  • anonymous
i know is sec = 1/ cos
anonymous
  • anonymous
Do you still need help solving for \(\theta\)?
anonymous
  • anonymous
yes..
anonymous
  • anonymous
Ok so we have \[\Large \frac{1}{\cos^2(\theta)} = 8\cdot \cos(\theta)\]How can we isolate \(\theta \) further?
anonymous
  • anonymous
what will happen next?? no idea. -_-
anonymous
  • anonymous
How about we multiply both sides by \(\cos^2(\theta)\)? Try that.
anonymous
  • anonymous
then it will become 1= 8 cos^3 theta ??
anonymous
  • anonymous
Yes! So what about getting rid of the coefficient?
anonymous
  • anonymous
1/8 = cos ^3 theta ??
anonymous
  • anonymous
Now it's just algebra. We learned that long ago.
anonymous
  • anonymous
How do you get rid of an exponent?
anonymous
  • anonymous
hmm i dont know can u help about it?
anonymous
  • anonymous
Why don't you take the cubed root of both sides?
anonymous
  • anonymous
oww okay I get it :) THanks
anonymous
  • anonymous
Just remember that you want the smallest positive \(\theta \), and that \(\cos(\theta)\) must also be positive since they should be increasing.
anonymous
  • anonymous
Otherwise there would be many solutions!
anonymous
  • anonymous
I get theta = 60 is that correct?
anonymous
  • anonymous
@wio
anonymous
  • anonymous
Yes! http://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Unit_circle_angles_color.svg/300px-Unit_circle_angles_color.svg.png
anonymous
  • anonymous
Thank you :)
hartnn
  • hartnn
Great explanation @wio :)

Looking for something else?

Not the answer you are looking for? Search for more explanations.