Posted by **Greg** on Monday, October 8, 2012 at 9:03am.

Find the exact value of thet following trigonometric functions:

tan(5pi/6)

tan(7pi/6)

tan(11pi/6)

- Precalculus/Trig 5 -
**Reiny**, Monday, October 8, 2012 at 9:26am
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

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