Precalculus : Pre-Calculus

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #14 : Convert Polar Equations To Rectangular Form And Vice Versa

Which is equivalent to in rectangular form?

Possible Answers:

Correct answer:

Explanation:

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

Possible Answers:

Correct answer:

Explanation:

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

Possible Answers:

Correct answer:

Explanation:

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

Possible Answers:

Correct answer:

Explanation:

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 ?

Possible Answers:

Correct answer:

Explanation:

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 ?

Possible Answers:

Correct answer:

Explanation:

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

Possible Answers:

Correct answer:

Explanation:

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

Possible Answers:

Correct answer:

Explanation:

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?

Possible Answers:

Correct answer:

Explanation:

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?

Possible Answers:

Correct answer:

Explanation:

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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