Question 337745: Find the rectangular equation of the curve whose parametric equations are: x=5cos 2t and y= -sin 2t, 0 =< t =< 180degrees Found 2 solutions by Fombitz, stanbon:Answer by Fombitz(32388) (Show Source):
You can put this solution on YOUR website! Find the rectangular equation of the curve whose parametric equations are:
x = 5cos(2t) and y = -sin(2t) , 0 =< t = < 180degrees
-----------------------------------------------------------
Solve the 1st equation for "t":
x = 5cos(2t)
cos(2t) = x/5
2t = invcos(x/5)
t = (1/2)invcos(x/5)
-------------------------
Substitute that t-value into the 2nd equation:
y = -sin(2[(1/2)invcos(x/5)])
y = -sin(invcos(x/5))
-----------
If invcos(x/5) is an angle whose cos is x/5
The sin of that angle is (sqrt(25-x^2))/5
---
So, y = -(1/5)sqrt(25-x^2)
5y = -sqrt(25-x^2)
Square both sides:
25y^2 = 25-x^2
x^2+25y^2 = 25
(x^2/25) + y^2 = 1
==========================
Cheers,
Stan H.
==========================
(