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
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
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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