Question

Help with the following question about continuous.

Answer 1

what is it?

Answer 2

\[S=\left\{ \left( x,y \right)\epsilon R ^{2}:x ^{2}+y ^{2} =1\right\}\]

Answer 3

so S is a circle so far ...

Answer 4

x, and y are continuous on all real numbers on a 2D plane, where you have a circle.

Answer 5

S is your circle, as amistre said up above.

Answer 6

Define \[h:[0,2\pi)\rightarrow S \] by \[h(\theta)=(\cos \theta,\sin)\]

Answer 7

prove that it is continuous and bijective , but it is not a homoemorphism

Answer 8

i think
\[h=\begin{pmatrix}cos\theta&sin\theta\\-sin\theta&cos\theta\end{pmatrix}\]

Answer 9

h maps a parametric function onto a cartesian relation ... (cos t, sin t) is the unit circle such that x=cos t, y = sin t

Answer 10

how to prove the stuff youve mentioned tho; i dont have a ready idea as of yet

Answer 11

what have you tried?

Answer 12

\[h(\theta)=(\cos \theta,\sin \theta)\]

Answer 13

i've realised that sin and cos it is continuous at every angle so since \[0\le \theta <2\]

Answer 14

i mean 2pi

Answer 15

@amistre64

Answer 16

@timo86m