Polar to Cartesian Equations

The video tutorial explains how to convert polar equations into Cartesian equations. It covers two examples: converting r = 3 csc(θ) to y = 3, a horizontal line, and r = -4 sec(θ) to x = -4, a vertical line. The tutorial includes step-by-step instructions for substitution and simplification, and concludes with a graphical verification of the results.

What is the first step in converting a polar equation to a Cartesian equation?

• Graph the polar equation

• Express the equation in terms of x and y

• Identify the polar coordinates

• Find the reciprocal of the trigonometric function

How is cosecant θ related to sine θ?

• Cosecant θ is the square of sine θ

• Cosecant θ is the reciprocal of sine θ

• Cosecant θ is the inverse of sine θ

• Cosecant θ is the same as sine θ

What is the Cartesian equation derived from r = 3 cosecant θ?

• x = 0

• y = 3

• y = 0

• x = 3

What does the Cartesian equation y = 3 represent?

• A circle with radius 3

• A diagonal line through the origin

• A horizontal line at y = 3

• A vertical line at x = 3

What is the purpose of multiplying both sides by sine θ in the first example?

• To clear the denominator

• To convert to Cartesian coordinates

• To eliminate the variable r

• To simplify the equation

What is the relationship between secant θ and cosine θ?

• Secant θ is the inverse of cosine θ

• Secant θ is the same as cosine θ

• Secant θ is the reciprocal of cosine θ

• Secant θ is the square of cosine θ

What is the Cartesian equation derived from r = -4 secant θ?

• y = 0

• y = -4

• x = -4

• x = 0

What does the Cartesian equation x = -4 represent?

• A diagonal line through the origin

• A circle with radius 4

• A horizontal line at y = -4

• A vertical line at x = -4

In the second example, what is the result of multiplying both sides by cosine θ?

• The equation becomes undefined

• The equation remains unchanged

• The equation becomes a circle

• The equation simplifies to x = -4

What is verified graphically at the end of the tutorial?

• Both equations result in a vertical and a horizontal line

• Both equations result in a horizontal line

• Both equations result in a diagonal line

• Both equations result in a circle