anonymous
  • anonymous
Find the exact value of tan inverse
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
UnkleRhaukus
  • UnkleRhaukus
tan theta = opp / adj
UnkleRhaukus
  • UnkleRhaukus
(there is no inverse)

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More answers

anonymous
  • anonymous
this is a dumb question.. but what does the theta sign look like?
UnkleRhaukus
  • UnkleRhaukus
theta : \(\theta\)
anonymous
  • anonymous
that's the sign I used but I thought it meant inverse :0
UnkleRhaukus
  • UnkleRhaukus
\[\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\]\[\Downarrow\]\[\theta = \tan^{-1}\left(\frac{\text{opposite}}{\text{adjacent}}\right)=\arctan\left(\frac{\text{opposite}}{\text{adjacent}}\right)\]
UnkleRhaukus
  • UnkleRhaukus
the question is only asking you to find \(\tan\theta\), you don't have to compute the value of theta,
anonymous
  • anonymous
It's saying the equation has too many equal signs
UnkleRhaukus
  • UnkleRhaukus
what is the length of the side opposite to theta in the diagram?
anonymous
  • anonymous
is 6 the opp and 2 and 5 the adj?
UnkleRhaukus
  • UnkleRhaukus
yes, opp = 6 and adj = 2√5
anonymous
  • anonymous
my calculator said it was 1/2 as the answer, but it said that 1/2 is not correct
UnkleRhaukus
  • UnkleRhaukus
\(\tan\theta = \dfrac{6}{2\sqrt 5}\)
UnkleRhaukus
  • UnkleRhaukus
now cancel the common factor
anonymous
  • anonymous
what's the common factor?
UnkleRhaukus
  • UnkleRhaukus
\[\tan\theta = \dfrac{6}{2\sqrt 5}=\dfrac{2\times3}{2\times\sqrt 5}=\]
anonymous
  • anonymous
\[\tan \emptyset \frac{ 6}{ 5 }=\frac{ 3 }{ 5 }\]
UnkleRhaukus
  • UnkleRhaukus
now rationalize the denominator \[\tan\theta = \frac{6}{2\sqrt 5}=\frac{3}{\sqrt 5}=\frac{3}{\sqrt 5}\times\frac{\sqrt5}{\sqrt5}=\]
anonymous
  • anonymous
20..?
UnkleRhaukus
  • UnkleRhaukus
\[\frac{3}{\sqrt 5}\times\frac{\sqrt5}{\sqrt5}=\frac{3\times\sqrt5}{\sqrt5\times\sqrt5}\] now simplify the denominator
anonymous
  • anonymous
would it be 1 because 5 can go into 5 once?
UnkleRhaukus
  • UnkleRhaukus
\[\sqrt5\sqrt5=\sqrt5^2= .....\]
anonymous
  • anonymous
i'm not even sure how to go about that :o
UnkleRhaukus
  • UnkleRhaukus
\[√x^2 = x\]
anonymous
  • anonymous
oh gosh
UnkleRhaukus
  • UnkleRhaukus
ikr
anonymous
  • anonymous
anonymous
  • anonymous
my options don't even make sense then
UnkleRhaukus
  • UnkleRhaukus
we are very close to one of those
UnkleRhaukus
  • UnkleRhaukus
what is the square root of five squared?
anonymous
  • anonymous
5? I think
anonymous
  • anonymous
oh wait i did that wrong
UnkleRhaukus
  • UnkleRhaukus
yes, so what is our final answer?
anonymous
  • anonymous
5 squared over
anonymous
  • anonymous
3 I wanna say

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