Question

please help. Why does my professor say that the equation of a circle with radius 1 centered at the origin equals: r=cos(theta)+sin(theta)

Answer 1

he doesn't

Answer 2

first off, if the radius is \(1\) then \(r=1\) not \(r\)

Answer 3

I know this. I should state that its in vector form, with r=cos(theta)i+sin(theta)j

Answer 4

I dont understand why this equals a circle centered at the origin. I thought it should be r=cos(theta)^2i+sin(theta)^2j

Answer 5

I guess I dont understand. I am plugging it into wolfram and it shows me a circle of radius 1 but centered at (1,1)

Answer 6

\(a=r\cos(\theta), b = r\sin(\theta)\)

Answer 7

so he is correct. Why does wolfram show me something completely different?

Answer 8

\[ai+bj=r\cos(\theta)i+r\sin(\theta)j\]

Answer 9

the magnitude of r is 1

Answer 10

not always
\(r\) could be anything

Answer 11

so a function: \[r=\cos (\theta)i + \sin(\theta)j\] is correct

Answer 12

but the radius of my circle is 1

Answer 13

i may be wrong but what you wrote doesn't make sense to me
what is \(r\) supposed to be? is it supposed to be 1?

Answer 14

maybe what he/she was saying is \(a+bi=r\cos(\theta)i+r\sin(\theta)j\)

Answer 15

so basically I have a quarter circle in the first quadrant, as illustrated: