plot the given polar coordinate and find three additional polar representations of the point. (3, (5*pi) /6))
To plot the given polar coordinate (3, (5π)/6), we can use the following steps:
1. Start at the origin of a polar coordinate system, which is the point (0,0).
2. Move along the positive x-axis (also called the polar axis) until you reach the angle specified by (5π)/6 or 150 degrees.
3. From the end point, move towards the angle by moving along the radius of length 3 units.
Plotting the point should give you a visual representation.
To find three additional polar representations of the point, we can add or subtract integer multiples of 2π (360 degrees) to the angle. Here are the additional polar representations:
1. (3, (5π)/6 + 2π) = (3, 13π/6) - This adds one complete revolution to the original angle, giving us an equivalent point.
2. (3, (5π)/6 + 4π) = (3, 21π/6) - This adds two complete revolutions to the original angle, giving us another equivalent point.
3. (3, (5π)/6 - 2π) = (3, -11π/6) - This subtracts one complete revolution from the original angle, giving us yet another equivalent point.
These three additional polar representations have the same magnitude (3 units) but have different angles that differ by a multiple of 2π.