113k views
3 votes
If \theta is an angle in standard position and its terminal side passes through the point (-15,-8), find the exact value of cot\theta in simplest radical form.

1 Answer

5 votes

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.

__

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.

<95141404393>

User Chris Ritchie
by
7.6k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories