Write Equation in Polar

[greatwhiteshark]

The letters x and y represent rectangular coordinates. Write each equation using polar coordinates.

x^2 = 4y

My work:

NOTE: t = theta

x = rcost

y = rsint

I pluggued these values into the equation given.


(rcost)^2 = 4(rsint)

This is where I get stuck.

 

[soroban]

Hello, greatwhiteshark!

Write each equation using polar coordinates: . x² = 4y

My work: .x = r cos θ, .y = r sin θ

I plugged these values into the equation given.
. . . (r cos θ)² = 4(r sin θ) . . . . correct!

This is where I get stuck.

Well, sometimes we can solve for r . . . sometimes, we can't.

We have: . r²cos²θ . = . r sin θ

Divide by r: . r cos²θ . = . sin θ

. . . . . . . . . . . . . . . . . . . . .1 . . . sin θ
Divide by cos²θ: . r . = . ------- . -------
. . . . . . . . . . . . . . . . . . . cos θ . .cos θ

Therefore: . r . = . sec θ tan θ

 

[greatwhiteshark]

soroban

I follow your steps except for number 4. Where did number 4 (you know, 4(rsintheta) vanish to?

 

[soroban]

*blush* . . . I just <u>forgot</u> the 4 . . . sorry!

 

[greatwhiteshark]

okay

Got it.