Pre-Calculus Prep: Graphing Polar Coordinates (3, 150 Degrees) and (2, -255 Degrees)

In pre-calculus, graphing polar coordinates allows us to represent points in a plane using radial distance (r) and angular measure (θ). Let's explore the polar coordinates (3, 150 degrees) and (2, -255 degrees) and graph them.

1. Understand the polar coordinate system: In polar coordinates, a point is represented by an ordered pair (r, θ), where r represents the distance from the origin to the point and θ represents the angle (in degrees or radians) measured counterclockwise from the positive x-axis.

2. Plotting the first point (3, 150 degrees):
- Start at the origin (0, 0) on the coordinate plane.
- Move outward from the origin to a distance of 3 units.
- Rotate counterclockwise from the positive x-axis by an angle of 150 degrees.
- Mark the point reached as (3, 150 degrees).

3. Plotting the second point (2, -255 degrees):
- Start at the origin (0, 0) on the coordinate plane.
- Move outward from the origin to a distance of 2 units.
- Rotate counterclockwise from the positive x-axis by an angle of 255 degrees.
- Mark the point reached as (2, -255 degrees).

4. Shape of the graph:
- For the first point (3, 150 degrees), the distance from the origin is 3 units, and the angle is 150 degrees. This places the point in the second quadrant, with an angle of 150 degrees measured counterclockwise from the positive x-axis.
- For the second point (2, -255 degrees), the distance from the origin is 2 units, and the angle is -255 degrees. This places the point in the fourth quadrant, with an angle of -255 degrees measured counterclockwise from the positive x-axis.

5. Optional: You can connect the plotted points to visualize any patterns or shapes that may emerge from the graphed polar coordinates. In this case, since we only have two points, it may not reveal a clear pattern or shape.

Remember to label the axes, indicate any relevant coordinates or points on the graph, and use a suitable scale for your coordinate plane.

By following these steps and graphing the polar coordinates (3, 150 degrees) and (2, -255 degrees), you can plot these points on a polar coordinate system in pre-calculus.
These videos are designed to review and reteach Precalculus and Collegeboard Pre-CALC AP content. My videos cover functions, polynomials, exponential and logarithmic expressions, trigonometry, parametric equations, polar coordinates, vectors, matrices and systems, conic sections, discrete mathematics, sequences and series; and an introduction to calculus.

Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa .
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