Question

tan -1 square root 3/3 find exact value of expression (unit circle problem)

Answer 1

\[\tan^{-1}(\sqrt[3]{3})\] This?

Answer 2

or this? \[\tan^{-1}\left(\sqrt{\frac{3}{3}}\right)\]

Answer 3

number two

Answer 4

Well 3/3 is 1, and the sqare root of 1 is 1, so it's asking for the arctan(1). Where on the unit circle (within the range of the arctan) is the tangent equal to 1? Remember, the tangent is the opposite over adjacent. If that's equal to 1, it means the opposite and adjacent are the same.

Answer 5

Surely it's ArcTan[Sqrt[3]/3], yes?

Answer 6

the whole things not squared just the the first 3 and no arc tan just regular tan

Answer 7

Why did you put the -1 above the tan? \[\tan^{-1} = \arctan\]They're the same thing, just different notation

Answer 8

oh then yea arc tan lol sorry

Answer 9

So it wants you to find the angle who's tangent is sqrt(3)/3 <--btw, using parenthesis would avoid all this confusion

sqrt(3)/3 can be rewritten as:\[\frac{\sqrt{3}}{3} = \frac{1}{\sqrt{3}}\]by multiplying both the numerator and the denominator by sqrt(3).

The tangent is opposite over adjacent, so if you think about this angle's triangle, it would look like this:If you remember your special triangles, you should notice that this is a 30-60-90 triangle, and theta is pi/6. So \[\arctan(\frac{\sqrt{3}}{3}) = \frac{\pi}{6}\]