## asapbleh 4 years ago Find tan theta. Please see below for equation.

1. anonymous

??

2. asapbleh

$\tan \theta=+\sqrt{1-\sec ^2theta}$ tan theta= $\sqrt{-8}$ does squareroot of -8 equal to $1/2\sqrt{2}$ ?

3. anonymous

no

4. asapbleh

why?

5. anonymous

$\sqrt{-8}=i 2\sqrt{2}$

6. asapbleh

Ok, heres the full question: Find tan theta if sin theta =1/3 and theta is in quadrant I.

7. anonymous

easy ...just use triangle...it'll help you forever |dw:1347169230431:dw| and tan theta= 1/2sqrt2

8. anonymous

$\tan \theta= \frac{ 1 }{ 2 \sqrt2 }$

9. asapbleh

I'm saying how do you get $1/2\sqrt{2}$?

10. anonymous

use pythagoraas....

11. asapbleh

I need to use the equation: $\tan \theta=\sqrt{1-\sec ^2theta}$

12. anonymous

$3^2=1^2+x^2....x= \sqrt{3^2-1}=\sqrt 8$

13. anonymous

don't use that....if you have to use that find another side first

14. asapbleh

if so, how do i find the other side?

15. anonymous

use pythagoras.....as i have stated above

16. asapbleh

ok, then if i need to find csc theta, if cot theta = -21/20 and sin theta>0 then would my answer be $\sqrt{1+21/20}$ or

17. anonymous

from above triangle cot theta= 2 sqrt 2

18. asapbleh

im sorry, this is another problem, not the above triangle

19. anonymous

i just explained the easiest method to find out any answer

20. anonymous

see you have sin theta= 1/3 now 1 is perpendicular and 3 is hypotenuse now use pythagoras theorem to find another side and since you have three sides you can find any of the trigonometric value

21. asapbleh

ok, so is it .6.40?

22. anonymous

what another side?

23. asapbleh

I dont seem to have another side

24. anonymous

another side would be ^2=1^2+x^2 x^2=9-1=8 x=2sqrt2

25. asapbleh

Problem: Find csc theta if cot theta=-21/20 and sin theta>0 if i use the pythagoreas, then would it be 20^2+x^2=21^2 ?

26. anonymous

okay wait

27. anonymous

square both sides. multiply through by sin^2 solve for tan

28. anonymous

$cosec^2 \theta=\cot^2 \theta-1$

29. asapbleh

omg, so ive been doing it wrong? ive been using $\csc \theta=\sqrt{1-\cot ^2\theta}$