Answer:
c. 5/4
Explanation:
The mnemonic SOH CAH TOA reminds you of the relationships involved in the cosine function:
... Cos = Adjacent/Hypotenuse
Your terminal ray with endpoint coordinates (4, -3) has a length (hypotenuse) given by the Pythagorean theorem as ...
... h = √(4² +(-3)²) = √25 = 5
The side adjacent to the angle is the x-axis, and its measure to the ray endpoint is 4. A picture, as in the first attachment, may help.
Then the cosine is the ratio of these:
... cos(θ) = adjacent/hypotenuse = 4/5
The secant is the reciprocal of the cosine:
... sec(θ) = 1/cos(θ) = 1/(4/5)
... sec(θ) = 5/4
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The second attachment shows how the signs of the trig functions vary according to quadrant. Your 4th-quadrant angle will have a positive secant.