Converting Coordinates: Polar and Rectangular Forms

The video tutorial covers the conversion of coordinates between polar and rectangular forms. It begins with an introduction to the basic concepts and formulas used in the conversion process. The tutorial then explains how to convert from polar to rectangular coordinates using the radius and angle, followed by a demonstration of converting from rectangular to polar coordinates using the hypotenuse and angle calculations. Practical examples and exercises are provided to reinforce the learning, ensuring a comprehensive understanding of the topic.

What is the formula for the x-coordinate in a polar to rectangular conversion?

• r * sin(theta)

• r * cos(theta)

• x / r

• y / r

In the example given, what is the rectangular coordinate for the polar point (5, pi/4)?

• (5 * sqrt(3)/2, 5 * sqrt(3)/2)

• (5, 0)

• (5 * sqrt(2)/2, 5 * sqrt(2)/2)

• (5, 5)

Which trigonometric function is used to find the y-coordinate in a polar to rectangular conversion?

• secant

• sine

• tangent

• cosine

What is the formula to find the radius when converting from rectangular to polar coordinates?

• sqrt(x^2 + y^2)

• x / y

• x^2 + y^2

• y / x

How do you determine the angle theta when converting from rectangular to polar coordinates?

• tangent inverse of y/x

• sine inverse of y

• secant inverse of x/y

• cosine inverse of x

What is the rectangular coordinate for the polar point (2, pi)?

• (-2, 0)

• (0, -2)

• (0, 2)

• (2, 0)

In the advanced example, what is the angle in degrees for the rectangular point (-1, 1) when converted to polar coordinates?

• 45 degrees

• 90 degrees

• 135 degrees

• 180 degrees

What is the polar coordinate for the rectangular point (-1, 1)?

• (1, pi)

• (sqrt(2), 3pi/4)

• (sqrt(2), pi/4)

• (1, pi/2)

Which quadrant is the angle -45 degrees located in when converting from rectangular to polar coordinates?

• Quadrant IV

• Quadrant III

• Quadrant II

• Quadrant I

What is the reference angle for -45 degrees when converting to polar coordinates?

• 90 degrees

• 60 degrees

• 45 degrees

• 30 degrees