SOLUTION: Transform the following equation to a cartesian equation: r=sec(theta)tan^2(theta)

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Question 1191359: Transform the following equation to a cartesian equation: r=sec(theta)tan^2(theta)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Transform the following equation to a cartesian equation:
r=sec%28theta%29%2Atan%5E2%28theta%29
First convert the expression into terms of cos%28theta%29+and sin%28theta%29...............sec%28theta%29=1%2Fcos%28theta%29+and tan%5E2%28theta%29=sin%5E2%28theta%29%2Fcos%5E2%28theta%29

r=%281%2Fcos%28theta%29+%29%28sin%5E2%28theta%29%2Fcos%5E2%28theta%29%29

r=sin%5E2%28theta%29%2Fcos%5E3%28theta%29

r%2Acos%5E3%28theta%29=sin%5E2%28theta%29

Now the normal substitutions are:
x=r%2Acos%28theta%29 =>cos%28theta%29=x%2Fr
and
y=r%2Asin%28theta%29 =>sin%28theta%29=y%2Fr

Substituting these values into the expression above gives

r%2A%28x%2Fr%29%5E3=%28y%2Fr%29%5E2
r%2A%28x%5E3%2Fr%5E3%29=y%5E2%2Fr%5E2
x%5E3%2Fr%5E2=y%5E2%2Fr%5E2
x%5E3=y%5E2