How do I find the value of sec(-pi)?

1 Answer
Alan P.
Sep 6, 2015

sec(-pi) = -1

Explanation:

Using a unit circle in standard position,
the angle (-pi) is a semicircle with its terminal point on the negative X-axis (at (x,y) = -1,0)

The length of the hypotenuse will be
color(white)("XXX")sqrt((-1)^2+0^2) = 1

and since the definition of sec is
color(white)("XXX")sec = ("hypotenuse")/("x-coordinate") (of unit circle)

sec(-pi) = 1/(-1) = -1

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