qadirabarnes70
Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Connect with a community of experts ready to help you find accurate solutions to your questions quickly and efficiently. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

5. Convert the rectangular equation x² + y² - 6y = 0 into a polar equation.
A. r = 6 sin theta
B. r = 6 cos theta
C. r = √6 sin theta
D. r = √6 cos thea​

Sagot :

Hrishii

Answer:

A. r = 6 sin theta

Step-by-step explanation:

Given equation is: [tex]x^2+y^2-6y=0[/tex]....(1)

Using the formulae that link Cartesian to Polar coordinates.

[tex]x=r\cos\theta \: and \: y = r\sin\theta[/tex]

Plugging the values of x and y in equation (1), we find:

[tex](r\cos\theta)^2+(r\sin\theta)^2-6(r\sin\theta)=0[/tex]

[tex]\implies r^2\cos^2\theta+r^2\sin^2\theta-6r\sin\theta=0[/tex]

[tex]\implies r^2(\cos^2\theta+\sin^2\theta)=6r\sin\theta[/tex]

[tex]\implies r^2(1)=6r\sin\theta[/tex]

[tex](\because \cos^2\theta+\sin^2\theta=1)[/tex]

[tex]\implies\frac{ r^2}{r}=6\sin\theta[/tex]

[tex]\implies\huge{\purple{ {r}=6\sin\theta}}[/tex]

We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.