Answer:
-√17/4
Explanation:
Because both the x- and the y-coordinates of (-4, -1) are negative, the angle, theta, is in Quadrant III.
tan theta = opp/adj = vertical side / horizontal side = 4/1, or just 4.
The two coordinates are the legs (both shorter than the hypotenuse) of the triangle formed by this terminal side / point.
The length of the hypotenuse is found using the Pythagorean Theorem and is:
√[ (1)² + (4)² = √17.
Again remembering that our terminal side is in Quadrant III,
sin Ф = opp/hyp = -1/√17
cos Ф = adj/hyp = -4/√17
tan Ф = opp/adj = 4 (see discussion above)
The instructions are to "find sec(theta)." The sec function is the inverse of the cos function. Here cos Ф = -4/√17, and so the secant of this angle is
the inverse (reciprocal) of the cosine, and is thus -√17/4