x= cos (t/2) y= sin (t) = sin(t/2+t/2) = 2sin (t/2) cos (t/2) y/x= 2sin (t/2) because of the fact that cos (t/2) = x/a million ( adjoining section /hypotenuse) ( Draw a suitable triangle ) opposite section is b= sqrt (a million-x^2) sin (t/2) = sqrt (a million-x^2) /a million for that reason y/x= 2sqrt (a million-x^2) take /^2 y^2 = 4x^2 (a million-x^2) 4x^4 -4x^2+y^2 =0
Comments
x = sin(t) so t = arcsin(x)
Plug into y:
y = cos(2arcsin(x))
Apply the given trig identity:
y = 1 - 2sin²(arcsin(x))
Simplify:
y = 1 - 2x²
x= cos (t/2) y= sin (t) = sin(t/2+t/2) = 2sin (t/2) cos (t/2) y/x= 2sin (t/2) because of the fact that cos (t/2) = x/a million ( adjoining section /hypotenuse) ( Draw a suitable triangle ) opposite section is b= sqrt (a million-x^2) sin (t/2) = sqrt (a million-x^2) /a million for that reason y/x= 2sqrt (a million-x^2) take /^2 y^2 = 4x^2 (a million-x^2) 4x^4 -4x^2+y^2 =0