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

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    0
    2021-10-12T08:28:01+00:00

    Answer:

    -√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

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