Converting Polar to Rectangular Equations

The video tutorial explains the conversion between polar and rectangular coordinate systems. It covers the mathematical relationships and formulas needed for conversion, such as the Pythagorean theorem and trigonometric identities. Through four examples, the tutorial demonstrates how to convert polar equations to rectangular form, including handling angles and using trigonometric functions like sine, cosine, and secant.

What is the relationship between x, y, and R in polar coordinates?

• x^2 + y^2 = R^2

• x^2 - y^2 = R^2

• x^2 - y^2 = 2R

• x^2 + y^2 = 2R

How do you express R in terms of x and y?

• R = sqrt(x^2 - y^2)

• R = x - y

• R = sqrt(x^2 + y^2)

• R = x + y

What is the tangent of theta in terms of x and y?

• tan(theta) = x^2/y^2

• tan(theta) = y^2/x^2

• tan(theta) = y/x

• tan(theta) = x/y

How can you express x in terms of R and theta?

• x = R * sin(theta)

• x = R * cos(theta)

• x = R / sin(theta)

• x = R / cos(theta)

What is the formula for y in terms of R and theta?

• y = R / cos(theta)

• y = R / sin(theta)

• y = R * cos(theta)

• y = R * sin(theta)

In the example R = 8 sin(theta), what is the first step to convert to rectangular form?

• Subtract R from both sides

• Add R to both sides

• Multiply both sides by R

• Divide both sides by R

What does R sin(theta) equal in rectangular coordinates?

• y

• x

• R

• theta

What is the standard form of the equation of a circle derived from R = 8 sin(theta)?

• (x + 4)^2 + y^2 = 16

• x^2 + (y - 4)^2 = 16

• (x - 4)^2 + y^2 = 16

• x^2 + (y + 4)^2 = 16

What is the rectangular form of a circle with center (0, 4) and radius 4?

• (x + 4)^2 + y^2 = 16

• x^2 + (y - 4)^2 = 16

• (x - 4)^2 + y^2 = 16

• x^2 + (y + 4)^2 = 16

In the example theta = PI/6, what is the tangent of PI/6?

• 1

• sqrt(3)/3

• sqrt(3)/2

• 1/2