Question

Turns out that I'm going to need help with this question. I wasn't able to figure it out on my own. Thanks for the help!

Answer 1

r = 1

Explanation:

The usual translation between rectangular coordinates and polar coordinates is ...

• x = r·cos(θ)
• y = r·sin(θ)

Substituting these into your equation, you get ...

(r·cos(θ))² + (r·sin(θ))² = 1

r²(cos(θ)² +sin(θ)²) = 1 . . . . . . factor out r²

r²(1) = 1 . . . . . . . . . . . . . . . . . . use the trig identity cos(θ)² +sin(θ)² = 1

r = 1 . . . . . . . take the square root

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It's that simple. Just as x=1 describes a line in Cartesian coordinates, r=1 describes a circle in polar coordinates.

Answer 2

r=1

Explanation:

x^2 +y^2 =1

We know that x^2 + y^2 = r^2

Replacing that in the equation

r^2 =1

Taking the square root of each side

sqrt(r^2) = sqrt(1)

r =1

The other way is to replace x with r cos theta and y with r sin theta

(r cos theta)^2 + (r sin theta) ^2 =1

r^2 cos^2 theta + r^2 sin^2 theta = 1

Factor out r^2

r^2 (cos^2 theta + sin^2 theta) =1

We know cos^2 theta + sin^2 theta =1

r^2 (1) =1

r^2 =1