$$r = 6 \sin\theta + \cos\theta$$

$$x = r \cos\theta$$, \ y = r \sin\theta$

$$r = 6 / (\sin\theta + \cos\theta)$$

Substitute $$x = r \cos\theta$$ and $$y = r \sin\theta$$

$$r = 6 / (\sin\theta + \cos\theta)$$

Question 1

Given the equation $$x + y = 6$$, which of the following is the correct conversion to polar coordinates?

Accepted Answer

$$r = 6 \sin	heta + \cos	heta$$

Question 2

Which substitution is used to convert $$x$$ and $$y$$ from rectangular to polar coordinates?

Accepted Answer

$$x = r \cos	heta$$, \ y = r \sin	heta$

Question 3

If $$x + y = 6$$, what is the value of $$r in $$terms of $$	heta$$?

Accepted Answer

$$r = 6 / (\sin	heta + \cos	heta)$$

Question 4

A line in rectangular coordinates is given by $$x + y = 6. $$Which of the following best describes its graph in polar coordinates?

Accepted Answer

A straight line not passing through the origin

Question 5

Which of the following is a correct step in converting $$x + y = 6 to $$polar form?

Accepted Answer

Substitute $$x = r \cos	heta$$ and $$y = r \sin	heta$$

Question 6

If $$r = 6 / (\sin	heta + \cos	heta)$$, what is the value of $$r$$ when $$	heta = \frac{\pi}{4}$$?

Accepted Answer

$$r = 6 / (\frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2}) = 6 / \sqrt{2} = 3\sqrt{2}$$

Question 7

Which of the following is NOT a valid method for converting a rectangular equation to polar form?

Accepted Answer

Replace $$r$$ with $$x^2$$ + $$y^2$$

Question 8

A medical imaging device scans along the line $$x + y = 6. If $$the device uses polar coordinates, what is the equation it should follow?

Accepted Answer

$$r = 6 / (\sin	heta + \cos	heta)$$

Question 9

Which of the following real-world scenarios could be modeled by the equation $$x + y = 6 in $$polar coordinates?

Accepted Answer

The boundary of a region scanned by a radar

Question 10

If $$x + y = 6 is $$converted to polar form, which trigonometric identity is used in the denominator?

Accepted Answer

$$\sin	heta + \cos	heta$$

Converting Polar Equations to Rectangular Coordinates

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