# How do you evaluate sec(cot^-1(-2)) without a calculator?

Aug 11, 2016

$\frac{\sqrt{5}}{2}$

#### Explanation:

Let $a = {\cot}^{- 1} \left(- 2\right) \in Q 4$

Then, tan a=-1/2. cos will be positive and so is its reciprocal secant in

Q4.

The given expression is

$\sec a = \sqrt{1 + {\tan}^{2} a} = \sqrt{1 = {\left(- \frac{1}{2}\right)}^{2}} = \frac{\sqrt{5}}{2}$

If a is assumed to be in Q2, instead, the answer will be $- \frac{\sqrt{5}}{2}$.