All Precalculus Resources
Example Questions
Example Question #14 : Convert Polar Equations To Rectangular Form And Vice Versa
Which is equivalent to in rectangular form?
To convert from polar form to rectangular form, substitute in , , and . Equivalently, and :
Substituting these into the original polar equation, we get:
multiply the second two fractions
now multiply these fractions
square both sides
multiply both sides by the denominator
Example Question #15 : Convert Polar Equations To Rectangular Form And Vice Versa
Write the equation in rectangular form
To convert to rectangular form, it is easiest to first multiply both sides by r:
Now we can make the substitutions and :
We want to solve for y, so subtract x squared from both sides:
now take the square root of both sides
Example Question #16 : Convert Polar Equations To Rectangular Form And Vice Versa
Convert to rectangular form
First, multiply both sides by the denominator:
multiply both sides by r
Now we can make the substitutions and :
subtract y from both sides
square both sides
subtract y squared from both sides
we are trying to get this in the form of y=, so subtract from both sides
divide both sides by
simplify
or
Example Question #11 : Polar Coordinates
Convert the equation to rectangular form
First, multiply both sides by the denominator:
multiply both sides by r
To convert, make the substitutions , , and
subtract y from both sides
square both sides
subtract y squared from both sides
we want to get y by itself, so subtract from both sides
divide both sides by
Example Question #18 : Convert Polar Equations To Rectangular Form And Vice Versa
Which rectangular equation is equivalent to ?
First multiply both sides by the denominator:
multiply both sides by r
distribute
Now we can make the substitutions , and :
distribute
combine like terms
subtract 2 x squared from both sides
We want to complete the square on the right, so factor our the -2:
to complete the square, add inside the parentheses. This multiplied by the -2 outside the parentheses is , so this means we're actually subtracting from both sides:
add and to both sides:
multiply both sides by 8
Example Question #11 : Convert Polar Equations To Rectangular Form And Vice Versa
Which is the rectangular form for ?
First multiply both sides by the right denominator:
multiply both sides by r
distribute
Now we can start to convet to rectangular by making the substitutions , , and :
combine like terms:
subtract y from both sides, and re-order this in decending order of powers of y:
this is a quadratic, so we can use the quadratic equation to get y by itself:
The answer choice that works is
Example Question #20 : Convert Polar Equations To Rectangular Form And Vice Versa
Write the equation for in rectangular form
Multiply both sides by the right denominator:
multiply both sides by r
Now we can substitute in and to start converting to rectangular form:
subtract x from both sides
square both sides
multiply both sides by 4
subtract x squared from both sides
take the square root of both sides
Example Question #21 : Convert Polar Equations To Rectangular Form And Vice Versa
Write the equation for in rectangular form
First multiply both sides by cosine
Now we can make the substitutions and
add 2 to both sides
square both sides
multiply both sides by the denominator
distribute on the left side
subtract from both sides
factor out y squared
divide both sides by
take the square root
Example Question #21 : Convert Polar Equations To Rectangular Form And Vice Versa
Which is equivalent to in rectangular form?
Multiply both sides by r squared
Now we can substitute and
square both sides
Example Question #21 : Convert Polar Equations To Rectangular Form And Vice Versa
Which is equivalent to in rectangular form?
First multiply both sides by r:
Now make the substitutions and :
add to both sides
subtract x squared and y squared from both sides
square both sides
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