Question

Which is the polar form of the parametric equations x=5cos(theta) and y=5sin(theta) ?

a. r= 5(theta)
b. r= 5
c. r= 25 cos (theta) sin (theta)
d. r= 25cos^2 (theta) + 25sin^2 (theta)

Answer 1

The polar coordinates are (r,φ), where r=
`√(x^2+y^2)` and cosφ=
`\frac{x}{ \sqrt{x^(2) +y^(2) } }`, sinφ=
`\frac{y}{ \sqrt{ x^(2) + y^(2) } }`.
So, when we are counting r, we obtain that r=
`\sqrt{ x^(2) + y^(2) } = \sqrt{(5cos(theta))^(2)+(5sin(theta))^(2)} =`=
`\sqrt{25(cos(theta)^(2)+sin(theta)^(2)) } =√(25)=5 .`
That's why the polar form of the parametric equations is r=5 (the circle of radius 5) and the right answer is B.