## 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 one year ago one year ago

1. wio Group Title

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. bii17 Group Title

Diffrentiation with respect to time.. @wio

3. wio Group Title

So do you think you can find those derivatives, and then solve for $$\theta$$?

4. bii17 Group Title

$\sec^2 \theta =8 \cos \theta] 5. bii17 Group Title \[\sec^2 \theta =8 \cos \theta$

6. wio Group Title

Now, what is $$\sec^2(\theta )$$ in terms of $$\sin(\theta)$$ and $$\cos(\theta)$$?

7. bii17 Group Title

i know is sec = 1/ cos

8. wio Group Title

Do you still need help solving for $$\theta$$?

9. bii17 Group Title

yes..

10. wio Group Title

Ok so we have $\Large \frac{1}{\cos^2(\theta)} = 8\cdot \cos(\theta)$How can we isolate $$\theta$$ further?

11. bii17 Group Title

what will happen next?? no idea. -_-

12. wio Group Title

How about we multiply both sides by $$\cos^2(\theta)$$? Try that.

13. bii17 Group Title

then it will become 1= 8 cos^3 theta ??

14. wio Group Title

Yes! So what about getting rid of the coefficient?

15. bii17 Group Title

1/8 = cos ^3 theta ??

16. wio Group Title

Now it's just algebra. We learned that long ago.

17. wio Group Title

How do you get rid of an exponent?

18. bii17 Group Title

hmm i dont know can u help about it?

19. wio Group Title

Why don't you take the cubed root of both sides?

20. bii17 Group Title

oww okay I get it :) THanks

21. wio Group Title

Just remember that you want the smallest positive $$\theta$$, and that $$\cos(\theta)$$ must also be positive since they should be increasing.

22. wio Group Title

Otherwise there would be many solutions!

23. bii17 Group Title

I get theta = 60 is that correct?

24. bii17 Group Title

@wio

25. wio Group Title
26. bii17 Group Title

Thank you :)

27. hartnn Group Title

Great explanation @wio :)