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

Expert Answers

An illustration of the letter 'A' in a speech bubbles

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.`

 

Approved by eNotes Editorial Team

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial