Question

Find the exact value of thet following trigonometric functions:

tan(5pi/6)
tan(7pi/6)
tan(11pi/6)

Answer 1

You should be able to make a quick sketch of the following right-angled 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 x-axis
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