How do you evaluate $sec^-1(2)$ ?

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Answer 1 · 2016-08-13T11:02:52

$sec^{-1}(2) = pi/3$

Let the answer be $x$ .

Since $sec^{-1}(2) = x$ , $sec(x) = 2$ .

As secant is the reciprocal of the cosine function, i.e. $sec(x) = 1/cos(x)$ , the following must be true as well.

$1/cos(x) = 2$

Or $cos(x) = 1/2$ .

The range of $sec^{-1}(x)$ is $[0,pi/2) uu (pi/2,pi]$ .
The range of $cos^{-1}(x)$ is $[0,pi]$ .

Since the ranges are similar, we can find $x$ using

$x = cos^{-1}(1/2) = pi/3$

How do you evaluate sec^-1(2)sec^-1(2)?