Precalculus/Trig 5
posted by Greg on .
Find the exact value of thet following trigonometric functions:
tan(5pi/6)
tan(7pi/6)
tan(11pi/6)

You should be able to make a quick sketch of the following rightangled triangles
30°  60°  90° > π/6rad  π/3rad  π/2 > 1  √3  2
and
45°  45°  90° > π/4  π/4  π/2 > 1  1  √2
You should also know the CAST rule, that is, where are each of the basic trig functions + or 
I will do the second one for you
tan (7π/6)
If it helps you, let's do in degrees.
7π/6 = 7(π/6) = 7(30°) = 210°
Now 210° is in quad III and 30 from the xaxis
we know from the above triangles that
tan 30° = 1/√3
so in the third quadrant, by CAST, the tangent is positive,
thus tan 7π/6 = 1/√3
( you can of course check all your answers with a calculator)
do the others the same way