How do you find the exact value of #tan^-1sqrt3#?

1 Answer
Nov 1, 2016

This can either equal #240˚# or #60˚#.

Explanation:

First of all, you need to find the quadrants where tangent is positive. You can remember the signs of the trigonometric functions in the quadrants using the following rule.

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Tangent is positive in quadrants #I# and #III#.

Now take the special triangle possessing sides of length #1-sqrt(3)-2#.

#tantheta = "opposite"/"adjacent"#, so the opposite side must measure #sqrt(3)# and the adjacent side must measure #1#, because #tantheta = sqrt(3)#.

In the special triangle, the angle of #60˚# is opposite the side measuring #sqrt(3)#, so we know the reference angle of #theta# is #60^@#.

We mentioned earlier that tangent is positive in quadrants #I# and #III#, so #theta = 60˚ and 180˚ + 60˚ =240˚#

Hopefully this helps!