Why is "secant" in the third quadrant negative?

1 Answer
Apr 27, 2018

By definintion

Explanation:

If we think of a right triangle with vertical leg y and horizontal leg x and hypotenuse r with an angle theta where x and r intersect, we know that:
x=rcos(theta)
and
y=rsin(theta).

sec(x) = 1/cos(x) by definition, that is sec(x) = r/x
Since r is a radius, it must be positive, so sec(x) is negative anywhere x is negative. This is in Quadrants II and III.