asapbleh
  • asapbleh
Find tan theta. Please see below for equation.
Mathematics
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
??
asapbleh
  • asapbleh
\[\tan \theta=+\sqrt{1-\sec ^2theta}\] tan theta= \[\sqrt{-8}\] does squareroot of -8 equal to \[1/2\sqrt{2}\] ?
anonymous
  • anonymous
no

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

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