Question

Rewrite the following polar equation in rectangular form.r=7.6coso - 9sing

Answer 1

Given:

`r\text{ = }\frac{7}{6cos\theta\text{ -9sin}\theta}`

Step 1: Cross-Multiply

`6rcos\theta\text{ - 9rsin}\theta\text{ = 7}`

By definition:

`\begin{gathered} x\text{ = rcos}\theta \\ y\text{ = rsin}\theta \end{gathered}`

Step 2: Substitute the expression for x and y:

`6x\text{ - 9y = 7}`

Hence, the rectangular form of the given polar form:

6x - 9y = 7