asapbleh
Find tan theta. Please see below for equation.
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jasonxx
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??
asapbleh
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\[\tan \theta=+\sqrt{1-\sec ^2theta}\]
tan theta= \[\sqrt{-8}\]
does squareroot of -8 equal to \[1/2\sqrt{2}\]
?
jasonxx
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no
asapbleh
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why?
jasonxx
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\[\sqrt{-8}=i 2\sqrt{2}\]
asapbleh
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Ok, heres the full question:
Find tan theta if sin theta =1/3 and theta is in quadrant I.
jasonxx
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easy ...just use triangle...it'll help you forever |dw:1347169230431:dw| and tan theta= 1/2sqrt2
jasonxx
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\[\tan \theta= \frac{ 1 }{ 2 \sqrt2 }\]
asapbleh
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I'm saying how do you get \[1/2\sqrt{2}\]?
jasonxx
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use pythagoraas....
asapbleh
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I need to use the equation: \[\tan \theta=\sqrt{1-\sec ^2theta}\]
jasonxx
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\[3^2=1^2+x^2....x= \sqrt{3^2-1}=\sqrt 8\]
jasonxx
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don't use that....if you have to use that find another side first
asapbleh
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if so, how do i find the other side?
jasonxx
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use pythagoras.....as i have stated above
asapbleh
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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
jasonxx
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from above triangle cot theta= 2 sqrt 2
asapbleh
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im sorry, this is another problem, not the above triangle
jasonxx
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i just explained the easiest method to find out any answer
jasonxx
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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
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ok, so is it .6.40?
jasonxx
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what another side?
asapbleh
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I dont seem to have another side
jasonxx
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another side would be ^2=1^2+x^2
x^2=9-1=8
x=2sqrt2
asapbleh
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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 ?
jasonxx
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okay wait
Algebraic!
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square both sides.
multiply through by sin^2
solve for tan
jasonxx
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\[cosec^2 \theta=\cot^2 \theta-1 \]
asapbleh
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omg, so ive been doing it wrong? ive been using \[\csc \theta=\sqrt{1-\cot ^2\theta}\]