SOLUTION: Find an equation in x and y whose graph contains the points on the curve C. x = 5 sin t, y = 6 cos t; 0 ≤ t ≤ 2π

Algebra ->  Equations -> SOLUTION: Find an equation in x and y whose graph contains the points on the curve C. x = 5 sin t, y = 6 cos t; 0 ≤ t ≤ 2π      Log On


   

Question 818717: Find an equation in x and y whose graph contains the points on the curve C.
x = 5 sin t, y = 6 cos t; 0 ≤ t ≤ 2π
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
x = 5 sin t, y = 6 cos t
Solve the first equation for sin(t):
x%2F5+=+sin%28t%29
and the second equation for cos(t):
y%2F6+=+cos%28t%29
Square both sides of both equations:
%28x%2F5%29%5E2+=+sin%5E2%28t%29 , %28y%2F6%29%5E2+=+cos%5E2%28t%29
x%5E2%2F25+=+sin%5E2%28t%29 , y%5E2%2F36+=+cos%5E2%28t%29
Add the two equations together:
x%5E2%2F25+%2B+y%5E2%2F36+=+sin%5E2%28t%29+%2B+cos%5E2%28t%29
You might see now why we've done what we've done. The right side should be recognized as a 1:
x%5E2%2F25+%2B+y%5E2%2F36+=+1