Determine the trigonometric ratios of angles \tan 30\degree, \tan 60\degree.

Step 1: Draw a special right triangle with a 60° angle.
NOTE: A special right triangle 30\degree-60\degree-90\degree.
It's sides are 1, 2 and \sqrt{3}
Step 2: Recall the definition of tangent and calculate \tan\ 60\degree
DEFINITION: The tangent (tan) of an angle in a right triangle is a ratio.
It is the length of the opposite side(opp) divided by the
length of adjacent side (adj).
NOTE: The length of the opposite is \sqrt{3}
The length of the adjacent side is 1
\tan60\degree=\frac{opp}{adj}=\frac{\sqrt{3}}{1}
and
Step 3: Calculate \tan\ 30\degree
The length of the opposite side is 1
length of the adjacent side is \sqrt{3}
\tan30\degree=\ \frac{opp}{adj}
\tan30\degree=\frac{1}{\sqrt{3}}