How do you evaluate ${sec}^{- 1} (2)$ $sec^-1(2)$ without a calculator?

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Answer 1 · 2018-03-08T11:21:47

See below.

$sec x = \frac{1}{cos x}$ $secx =1/cosx$ :

If:

$sec x = 2 \Rightarrow \frac{1}{cos x} = 2$ $secx=2=>1/cosx=2$

$\frac{1}{cos x} = 2 \Rightarrow cos x = \frac{1}{2}$ $1/cosx=2=>cosx=1/2$

$x = arccos (cos x) = arccos (\frac{1}{2}) = \frac{π}{3}, \frac{5 π}{3}$ $x=arccos(cosx)=arccos(1/2)=pi/3 , (5pi)/3$

General solution:

$\frac{π}{3} + 2 π n$ $pi/3+2pin$

$\frac{5 π}{3} + 2 π n$ $(5pi)/3+2pin$

For integers $n$ $bbn$

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