sketch parameter curve

[red and white kop!]

sketch this curve given in terms of the parameter alpha
x = cos alpha, y = sin alpha
i got x= 0 for y = 1, -1 and y = 0 for x = 1,-1 but from here i dont know how to sketch the graph! any suggestions?

 

[BigGlenntheHeavy]

\(\displaystyle x \ = \ cos(\alpha), \ y \ = \ sin(\alpha)\)

\(\displaystyle x^{2}+y^{2} \ = \ cos^{2}(\alpha)+sin^{2}(\alpha) \ = \ 1\)

\(\displaystyle Hence, \ we \ have \ a \ circle \ centered \ at \ the \ origin \ with \ radius \ 1.\)

 

[red and white kop!]

why a circle?

 

[BigGlenntheHeavy]

\(\displaystyle x^{2}+y^{2} \ = \ 1 \ is \ the \ equation \ of \ a \ circle. \ If \ you \ didn't \ know \ that, \ you're \ over \ your \ head.\)

 

[red and white kop!]

if you say so

 

[BigGlenntheHeavy]

I not only say so, I know so.

 

[red and white kop!]

when you say 'X^2 + Y^2 = 1 is the equation of a circle', can you explain this more specifically? apparently this is very important but i never learnt that statement, im working on parametric equations with cartesian variables and differentiation of these equations, etc. what are the properties of this circle? is it important to future studying?