Question

If θ is an angle in standard position and its terminal side passes through the point (-4,-5), find the exact value of

cot
⁡
θ
cotθ in simplest radical form.

Answer 1

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Answer:

cot(θ) = 4/5

Explanation:

In the polar/rectangular coordinate representation (x, y) ⇔ (r; θ), we know that ...

(x, y) = (r·cos(θ), r·sin(θ))

From the various trig definitions and identities, we also know that ...

cot(θ) = cos(θ)/sin(θ) = (x/r)/(y/r) = x/y

For the given (x, y) = (-4, -5), the cotangent is ...

cot(θ) = -4/-5 = 4/5