Reference angles

[xc630]

Hi I am having toruble with these two problems. It says to express each of the folowing in terms of a reference angle.

a) tan 3

b) cot 5

This radian form throws me off. I am not sure hhere this is suppsoed to be on the unit circle. I would appreciate any help. Thanks.

 

[pka]

I hope that you know how the find reference angles in degrees:
Given an angle in x degrees then x’ is the reference angle.
$\displaystyle 90^ \circ < x < 180^ \circ \quad \Rightarrow \quad x' = 180^ \circ - x$
$\displaystyle 180^ \circ < x < 270^ \circ \quad \Rightarrow \quad x' = x - 180^ \circ$
$\displaystyle 270^ \circ < x < 360^ \circ \quad \Rightarrow \quad x' = 360^ \circ - x$

Well $\displaystyle 180^ \circ = \pi \approx 3.142$, $\displaystyle 270^ \circ = 3\pi /2 \approx 4.712$, and $\displaystyle 360^ \circ = 2\pi \approx 6.283$.

Thus tan(3) would have a reference angle is $\displaystyle \pi - 3$ because $\displaystyle 3 < \pi$.

 

[xc630]

But whow would do do cot 5 since 5 is greater than pi?

 

[xc630]

would it be 2pi -5?