Originally Posted by

**ticbol** sec[arctan(-2)]

sec is a trig function.

arctan(-2) is an angle, believe it or not. Let as call it theta.

It is an angle whose tan function value is -2 ........a negative value.

Tangent is negative in the 2nd and 4th quadrant, so arctan(-2), or theta, is in the 2nd or 4th quadrant.

** In the 2nd quadrant, the opp side is positive, while the adj side is negative.**

so, tan(theta) = -2 = (2) / (-1).

Meaning, the opp is 2, and the adj is -1.

You are asked to find sec(theta).

Sec = hyp / adj

You don't know the hypotenuse. So you solve for it by using the Pythagorean theorem.

(hyp)^2 = (opp)^2 +(adj)^2

(hyp)^2 = (2)^2 +(-1)^2 = 5

hyp = sqrt(5) -------------hyp is always positive.

So,

sec(theta) = sec[arctan(-2)] = sqrt(5) / (-1) = -sqrt(5) ------answer, in the 2nd quadrant.