Question

Convert r=7/(9sinθ−cosθ) to rectangular form.

Enter your answer in slope-intercept form by filling in the boxes. Enter values so that fractions are simplified.

Answer 1

y = (1/9)x + 7/9

Explanation:

Divide both sides by 9

y = x/9 + 7/9

y = (1/9)x + 7/9

Divide both sides by 9

y = x/9 + 7/9

y = (1/9)x + 7/9

Answer 2

r = 7/(9sinθ - cosθ)

to rectangular form is:

y = (1/9)x + 7/9

Explanation:

Given that

r = 7/(9sinθ - cosθ)

Consider the following polar-to-rectangular equivalents.

x² + y² = r²

x/r = cosθ

y/r = sinθ

So

r = 7/(9sinθ - cosθ)

Can be written as

r = 7/(9y/r - x/r)

r = 7/(1/r)(9y - x)

Multiplying through by (1/r)

1 = 7/(9y - x)

Multiplying through by (9y - x)

9y - x = 7

9y = x + 7

Divide both sides by 9

y = x/9 + 7/9

y = (1/9)x + 7/9

And this is the answer