## Ac3 one year ago Simplify the following expression.

1. Ac3

$\sqrt{(7xcosx)^2+(-7xsinx+14cosx)^2}$

2. Ac3

the farthest i got to was$\sqrt{49x^2-196sinxcosx+196\cos^2x}$

3. Ac3

We want the radical to go away if possible or get the least amount of terms under the radical at least.

4. Ac3

Any idea @Preetha ?

5. anonymous

if you are lucky it is a prefect square

6. anonymous

doesn't look like one though, maybe some other trick

7. Ac3

I factored out a 49 and pulled it out of the radical. I was thinking maybe a trig identity for cos^2x not sure though.

8. freckles

was that thing really the initial problem?

9. Ac3

Well if you want the initial problem I'll go ahead and give it to you.

10. anonymous

the 49 comes out for sure not sure what else you can do here

11. anonymous
12. anonymous

*is

13. Ac3

r(t)=(7tsint+7cost)i + 7j + (7tcost-7sint)k, Find the Tangential, Normal, Binormal, and the Torsion.

14. Ac3

I think that's as far as it's going to go if I pull out the 49.

15. freckles

tangential is just ... $|r'(t)| \text{ }$ $r'(t)=[7 \sin(t)+7t \cos(t)-7\sin(t)]i+[0]j+[7 \cos(t)-7 t \sin(t)-7 \cos(t)]k \\ r'(t)=7 t \cos(t) i -7t \sin(t) k$

16. freckles

$|r'(t)|=\sqrt{(7 t \cos(t))^2+(-7 t \sin(t))^2}$

17. freckles

this looks prettier

18. Ac3

wait hold on let me check your derivative because I checked mine like 4 times.

19. freckles

it looks like your k component was different

20. freckles

yeah seems like you wrote 7cos(t)-7 cos(t) as 7 cos(t)+7 cos(t) instead

21. Ac3

ahhhhhhhh i screwed up the last part!!!!!

22. Ac3

thanks freckles.

23. freckles

np

24. Ac3

derivative of -7sint = 7cost <--- lmfao i'm an idiot.

25. freckles

maybe for a sec you got antiderivative and derivative mixed up :p it happens to all of us especially on those crazy trig functions

26. Ac3

It happens to me all the time.

27. Ac3

I've been doing way too many integrals

28. freckles

29. Ac3

see ya man thx again!

30. freckles

peace