1. ## sketch parameter curve

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?

2. Originally Posted by furor celtica
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?
Obviously you are using degrees as argument of the trigonometric functions. So choose those values of $\displaystyle \alpha$ where you know the trig values:

$\displaystyle \alpha = 60^\circ \rightarrow x = \frac12, y = \pm \frac12 \sqrt{3}$

$\displaystyle \alpha = 30^\circ \rightarrow x = \frac12 \sqrt{3}, y = \pm \frac12$

and so on ...

3. not really, this is less trigonometry than solving equations involving a parameter and Cartesian variables!

4. Originally Posted by furor celtica
not really, this is less trigonometry than solving equations involving a parameter and Cartesian variables!
Given
$\displaystyle x = \cos(\alpha)$
$\displaystyle y=\sin(\alpha)$

Square both sides of both equations and add columnwise:

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

which is the equation of the unit circle around the origin.