What graph is traced by the equation (x, y) = (5sin 12t , 6−5 cos 12t)?Think of another equation that will produce the same graph. Use your calculator to check.

Answer 1

then
x = 5sin 12t
x/5 = sin 12t
12t = arcsin (x/5)

y = 6-5cos 12t
5cos 12t = 6-y
cos 12t = (6-y)/5
12t = arcsin (6-y)/5

construct a right angled triangle with hypotenuse 5, opposite as x, and adjacent at 6-y with a base angle of 12t

all the above would be true according to that triangle.
Also
x^2 + (6-y)^2 = 25
x^2 + 36 - 12y + y^2 = 25

x^2 + y^2 - 12y = -11

looks like the equation of a circle to me.