convert from parametric to rectangular?

knowing cos(2t)=1-2(sin^2(t))

convert these equations from parametric to rectangular:

x=sint and y=cos2t

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

Sign In or Register to comment.