Converting Rectangular Equations to Polar Equations

This video tutorial explains how to convert rectangular equations into polar equations. It begins by defining rectangular and polar equations, followed by key formulas needed for conversion. The tutorial provides several examples, demonstrating the conversion process step-by-step, including equations like x = 8, y = 5, and more complex forms such as x^2 + y^2 = 6x + 4y. The video emphasizes understanding the relationship between rectangular coordinates (x, y) and polar coordinates (r, theta) and using trigonometric identities to achieve the conversion.

Which of the following is an example of a rectangular equation?

• r = 7 sin(theta)

• x + y = 4

• theta = pi/3

• r = 4

What is the formula for x in terms of r and theta?

• x = r sin(theta)

• x = r sec(theta)

• x = r cos(theta)

• x = r tan(theta)

If x = 8, what is the polar form of this equation?

• r = 8 sin(theta)

• r = 8 csc(theta)

• r = 8 cos(theta)

• r = 8 sec(theta)

How do you express y = 5 in polar form?

• r = 5 sec(theta)

• r = 5 csc(theta)

• r = 5 cot(theta)

• r = 5 tan(theta)

What is the polar form of the equation 5x + 4y = 8?

• r = 8 / (5 cos(theta) + 4 sin(theta))

• r = 8 / (5 tan(theta) + 4 cot(theta))

• r = 8 / (5 sec(theta) + 4 csc(theta))

• r = 8 / (5 sin(theta) + 4 cos(theta))

What is the first step in converting x^2 + y^2 = 16 to polar form?

• Replace x^2 + y^2 with r^2

• Take the square root of both sides

• Replace x with r cos(theta)

• Replace y with r sin(theta)

How do you convert y^2 = 4x into polar form?

• r^2 sin^2(theta) = 4 r cos(theta)

• r^2 cot^2(theta) = 4 r csc(theta)

• r^2 cos^2(theta) = 4 r sin(theta)

• r^2 tan^2(theta) = 4 r sec(theta)

What is the polar form of x^2 = 8y?

• r = 8 cos(theta) sin(theta)

• r = 8 cot(theta) csc(theta)

• r = 8 sin(theta) cos(theta)

• r = 8 tan(theta) sec(theta)

In the equation y = sqrt(3)x, what is the value of theta?

• theta = pi/4

• theta = pi/2

• theta = pi/3

• theta = pi/6

What is the polar form of x^2 + y^2 = 6x + 4y?

• r = 6 cos(theta) + 4 sin(theta)

• r = 6 sec(theta) + 4 csc(theta)

• r = 6 sin(theta) + 4 cos(theta)

• r = 6 tan(theta) + 4 cot(theta)