## A point on the terminal side of an angle theta is given. Find the value of the indicated trigonometric function of theta. Given (-4,-

Question

A point on the terminal side of an angle theta is given. Find the value of the indicated trigonometric function of theta.
Given (-4,-1), find sec(theta)

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3 days 2021-10-12T08:26:55+00:00 1 Answer 0

-√17/4

Step-by-step 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