document.write( "Question 337745: Find the rectangular equation of the curve whose parametric equations are: x=5cos 2t and y= -sin 2t, 0 =< t =< 180degrees \n" ); document.write( "

Algebra.Com's Answer #242148 by stanbon(75887) $\"\"$ $\"About$

You can put this solution on YOUR website!
Find the rectangular equation of the curve whose parametric equations are:
\n" ); document.write( "x = 5cos(2t) and y = -sin(2t) , 0 =< t = < 180degrees
\n" ); document.write( "-----------------------------------------------------------
\n" ); document.write( "Solve the 1st equation for \"t\":
\n" ); document.write( "x = 5cos(2t)
\n" ); document.write( "cos(2t) = x/5
\n" ); document.write( "2t = invcos(x/5)
\n" ); document.write( "t = (1/2)invcos(x/5)
\n" ); document.write( "-------------------------
\n" ); document.write( "Substitute that t-value into the 2nd equation:
\n" ); document.write( "y = -sin(2[(1/2)invcos(x/5)])
\n" ); document.write( "y = -sin(invcos(x/5))
\n" ); document.write( "-----------
\n" ); document.write( "If invcos(x/5) is an angle whose cos is x/5
\n" ); document.write( "The sin of that angle is (sqrt(25-x^2))/5
\n" ); document.write( "---
\n" ); document.write( "So, y = -(1/5)sqrt(25-x^2)
\n" ); document.write( "5y = -sqrt(25-x^2)
\n" ); document.write( "Square both sides:
\n" ); document.write( "25y^2 = 25-x^2
\n" ); document.write( "x^2+25y^2 = 25
\n" ); document.write( "(x^2/25) + y^2 = 1
\n" ); document.write( "==========================
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
\n" ); document.write( "========================== \n" ); document.write( "

\n" );