Find the parameterization of the semi-circle given by x^2+y^2=255, y

Question

Find the parameterization of the semi-circle given by x^2+y^2=255, y<=0 in the xy-plane starting at the point (-15, 0) and ending at (15, 0)?

anonymous · Answer

Is it 225? (rather than 255)

Just the usual cos t sin t and restrict the domain between 0 and pi.

anonymous · Answer

$$x=a \cos(t) ............y=bsin(t)......... using 0<t<2\pi$$

anonymous · Answer

$$x=\sqrt{255}\cos(t)...............y=\sqrt{255}\sin(t)$$

anonymous · Answer

i believe estudier is correct
if y^2+x^2=225
cos^2(t)+sin^2(t)=1
15x=cos(t)
15y=sin(t)
Then you rescrict the domain to tE[0,pi]

anonymous · Answer

Sorry it's 225 not 255

anonymous · Answer

so x=15cos(t) and y=15sin(t) from 0 to pi

anonymous · Answer

when you said y<=0 the semi circle is below the x axis
this means at a certain point y needs to be -15
so we restrict the domain from 
t E [pi,2pi] not [0,pi]

anonymous · Answer

I see. I understand now. Thanks!

anonymous · Answer

welcome

anonymous · Answer

Ah, lower not upper half, good spot...