Find tan theta. Please see below for equation.

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Find tan theta. Please see below for equation.

Mathematics
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\[\tan \theta=+\sqrt{1-\sec ^2theta}\] tan theta= \[\sqrt{-8}\] does squareroot of -8 equal to \[1/2\sqrt{2}\] ?
no

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why?
\[\sqrt{-8}=i 2\sqrt{2}\]
Ok, heres the full question: Find tan theta if sin theta =1/3 and theta is in quadrant I.
easy ...just use triangle...it'll help you forever |dw:1347169230431:dw| and tan theta= 1/2sqrt2
\[\tan \theta= \frac{ 1 }{ 2 \sqrt2 }\]
I'm saying how do you get \[1/2\sqrt{2}\]?
use pythagoraas....
I need to use the equation: \[\tan \theta=\sqrt{1-\sec ^2theta}\]
\[3^2=1^2+x^2....x= \sqrt{3^2-1}=\sqrt 8\]
don't use that....if you have to use that find another side first
if so, how do i find the other side?
use pythagoras.....as i have stated above
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
from above triangle cot theta= 2 sqrt 2
im sorry, this is another problem, not the above triangle
i just explained the easiest method to find out any answer
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
ok, so is it .6.40?
what another side?
I dont seem to have another side
another side would be ^2=1^2+x^2 x^2=9-1=8 x=2sqrt2
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 ?
okay wait
square both sides. multiply through by sin^2 solve for tan
\[cosec^2 \theta=\cot^2 \theta-1 \]
omg, so ive been doing it wrong? ive been using \[\csc \theta=\sqrt{1-\cot ^2\theta}\]

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