Thread: parameter restrictions HELP ??

hey, i just realli realli dont understand the restrictions for parameters in trig
so for this question
4. x = 2cos theta , y = 2sin theta
and 0<theta<2 pi

the equation is x squared +y squared = 4

i understand that
but then the restriction is -2>x>2 only

i get that by drawing the cos graph there is a restriction on the y axis as the cos graph is between 2 and -2, but how du u no that the restriction is on the y axis and not on the x axis?
AND why isnt there a restriction for the sin graph, ?? why isnt therre a restriction placed with y ?

im SO LOST !!!
any helpp apreciated !!

Placing those restrictions on x will implicitly place the same restrictions on y, given the symmetry of the equation.

so we can see that y will have the same domain and range as x.

Some further reading:

Domain (mathematics) - Wikipedia, the free encyclopedia

Range (mathematics) - Wikipedia, the free encyclopedia