Values of tan

• Apr 13th 2009, 11:23 AM
carbonite
Values of tan
What values does x have?

$\displaystyle tanx=(-square root 3) / 3$

x1 = ?
x2 = ?

Thank you!
• Apr 13th 2009, 11:55 AM
Soroban
Hello, carbonite!

Quote:

What values does $\displaystyle \theta$ have? . $\displaystyle \tan\theta \:=\:-\frac{\sqrt{3}}{3}$
You're expected to know the trig values for 30° 60°, and 45°.
. . Or be able to figured them out . . .

We have: .$\displaystyle \tan\theta \:=\:-\frac{1}{\sqrt{3}} \:=\:\frac{opp}{adj}$

This could arise from two possible situations . . .
Code:

        *         :\       _ : \       √3 :  \         :  \ θ       ---+----*-------           -1
And we see that: .$\displaystyle \theta_1 \:=\:120^o \:=\:\tfrac{2\pi}{3}$

Code:

              |               |               |  1           ----*----+-------               |\θ  :  _               | \  : -√3               |  \ :               |  \:               |    *
And: .$\displaystyle \theta_2 \:=\:\text{-}\;\!60^o \:=\:\text{-}\tfrac{\pi}{3}$