`arcsec(-sqrt(2))` Evaluate the expression without using a calculator

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For a negative number `x` (actually, for `x` less than or equal to `-1` ) its arcsecant is such number `y` in `(pi/2, pi]` that  `sec(y) = x.` This number is unique.

This is the same as `cos(y) = 1/x,` for the given `x = -sqrt(2)` it is `-1/sqrt(2).` We...

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For a negative number `x` (actually, for `x` less than or equal to `-1` ) its arcsecant is such number `y` in `(pi/2, pi]` that  `sec(y) = x.` This number is unique.

This is the same as `cos(y) = 1/x,` for the given `x = -sqrt(2)` it is `-1/sqrt(2).` We know such angle, it is  `(3 pi)/4.`

So the answer is  `(3 pi)/4.`

 

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