Converting Polar to Rectangular Coordinates

This video tutorial explains how to convert points from polar coordinates to Cartesian coordinates. It begins by introducing the concept and setting up the problem. The first example demonstrates the conversion process using a specific point and angle, detailing the calculations for x and y coordinates. A reference triangle is used to find trigonometric values. The second example explores an alternative angle, showing the flexibility in choosing angles for conversion. The tutorial emphasizes understanding the process and using trigonometric functions to achieve accurate results.

What is the first step in converting polar coordinates to rectangular coordinates?

• Identify the point using rectangular coordinates

• Convert the angle to radians

• Identify the point using polar coordinates

• Find the distance from the origin

Which formula is used to calculate the x-coordinate from polar coordinates?

• x = r sin(θ)

• x = r tan(θ)

• x = r cos(θ)

• x = r sec(θ)

In the first example, what is the value of r?

• 2

• 3

• 4

• 5

What is the cosine of 150 degrees used in the first example?

• √3/2

• 1/2

• -√3/2

• -1/2

What are the rectangular coordinates obtained in the first example?

• (2, -2√3)

• (-2, 2√3)

• (-2√3, 2)

• (2√3, -2)

In the second example, what is the value of θ?

• -45 degrees

• 315 degrees

• 45 degrees

• 90 degrees

What is the sine of -45 degrees used in the second example?

• √2/2

• -1/√2

• 1/√2

• -√2/2

What is the x-coordinate for the second example?

• -1/2

• -√2/2

• √2/2

• 1/2

What is the y-coordinate for the second example?

• 1/2

• √2/2

• -√2/2

• -1/2

What are the rectangular coordinates obtained in the second example?

• (1/2, -1/2)

• (-√2/2, √2/2)

• (√2/2, -√2/2)

• (-1/2, 1/2)