Answer:
15/8
Explanation:
You want the cotangent of the angle in standard position whose terminal side passes through the point (-15, -8).
Polar coordinates
In polar coordinates, the point can be represented by ...
r∠θ = r·(cos(θ), sin(θ)) = (-15, -8)
That is, ...
r·cos(θ) = -15
r·sin(θ) = -8
Cotangent
The cotangent function is defined in terms of sine and cosine as ...
cot(θ) = cos(θ)/sin(θ)
We can multiply numerator and denominator by r, and a useful substitution becomes clear:
cot(θ) = (r·cos(θ))/(r·sin(θ))
cot(θ) = -15/-8 = 15/8
The exact value of cot(θ) is 15/8.
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Additional comment
The value of r in the above is √((-15)² +(-8)²) = √289 = 17. As we saw, this value is not needed for the cotangent function. No radicals are needed for any of the trig functions of this angle.
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