Understanding Polar to Cartesian Conversion

The video tutorial explains how to convert a polar equation into a Cartesian equation in slope-intercept form. It begins with a polar equation and uses cross multiplication to eliminate fractions. The tutorial then substitutes trigonometric functions to express the equation in terms of x and y, resulting in a Cartesian equation. Finally, it converts this equation into slope-intercept form and verifies the solution by checking the slope and y-intercept.

What is the initial form of the polar equation given in the problem?

• R = 5 / (9 sin Theta + 7 cos Theta)

• R = 5 * (9 sin Theta + 7 cos Theta)

• R = 5 + (9 sin Theta + 7 cos Theta)

• R = 5 - (9 sin Theta + 7 cos Theta)

What mathematical operation is used to eliminate fractions in the equation?

• Division

• Subtraction

• Addition

• Cross-multiplication

Which trigonometric function is replaced by y/R in the substitution process?

• tangent Theta

• cotangent Theta

• sine Theta

• cosine Theta

After substitution, what is the resulting equation before simplification?

• 9R sin Theta + 7R cos Theta = 5

• 9x + 7y = 5

• 9y + 7x = 5

• 9R + 7R = 5

What is the Cartesian equation obtained after simplification?

• 7x + 9y = 5

• 9x + 7y = 5

• 7y + 9x = 5

• 9y + 7x = 5

What is the first step in converting the Cartesian equation to slope-intercept form?

• Add 7x to both sides

• Subtract 7x from both sides

• Multiply both sides by 9

• Divide both sides by 9

What is the slope of the line in the slope-intercept form?

• 7/9

• -7/9

• -9/7

• 9/7

What is the y-intercept of the line in the slope-intercept form?

• -5/9

• 5/9

• 9/5

• -9/5

What does the negative slope of the line indicate about its direction?

• The line is increasing

• The line is vertical

• The line is horizontal

• The line is decreasing

How does the graph verify the correctness of the slope-intercept form?

• The line is horizontal

• The line is vertical

• The line is increasing

• The line is decreasing