1. ## curve sketching

A question that i have to do involves me sketching the following curve

4cost + (2+sint)i 0<=t<=2pi

I have a feeling that my solution is wrong as it seems a bit too simple?

All i did was sub 0 and pi for t to which i got the line 4+2i. Is this solution some kind of elipse centred at 2i with radius 4?

2. Originally Posted by piglet
A question that i have to do involves me sketching the following curve

4cost + (2+sint)i 0<=t<=2pi

I have a feeling that my solution is wrong as it seems a bit too simple?

All i did was sub 0 and pi for t to which i got the line 4+2i. Is this solution some kind of elipse centred at 2i with radius 4?
Are we to assume from that "i" that this is in the complex plane?

If we call the real axis the x-axis and the imaginary axis the y-axis, then this is the same as x= 4 cos(t) and y= 2+ sin(t)

Then $\frac{x}{4}= cos(t)$ and $y- 2= sin(t)$.

Square both of those equations and add them.

3. Originally Posted by HallsofIvy
Are we to assume from that "i" that this is in the complex plane?

If we call the real axis the x-axis and the imaginary axis the y-axis, then this is the same as x= 4 cos(t) and y= 2+ sin(t)

Then $\frac{x}{4}= cos(t)$ and $y- 2= sin(t)$.

Square both of those equations and add them.
Yes "i" is in the complex plane... thanks alot for your input