Give three additional polar coordinate pairs for the
Point B: (-3,2π/3).
-2 < π < 2
your statement -2 < π < 2 makes no sense, it simply becomes a false statement:
-2 < 3.14.. < 2
I will assume you meant:
-2π < Ø < 2π
the obvious one:
(3,-4π/3)
2 more:
(3,-π/3) , (3,5π/6)
To generate three additional polar coordinate pairs for the given point B: (-3,2π/3), we need to vary the values of the radius and angle while keeping the given angle within the range -2π to 2π.
1. Increase the radius:
- To obtain a larger radius, let's double the initial radius of -3.
- New polar coordinate pair: (−6,2π/3)
- Make sure the angle remains within the specified range. In this case, 2π/3 is already within the range of -2π to 2π.
2. Decrease the angle:
- Let's subtract π/3 from the given angle of 2π/3. This will give us a smaller angle within the specified range.
- New polar coordinate pair: (−3,π/3)
3. Combine a different radius and angle:
- Choose a new radius, such as -4, and pick a different angle within the specified range, e.g., π/4.
- New polar coordinate pair: (-4, π/4)
Therefore, three additional polar coordinate pairs for the point B: (-3, 2π/3) are:
(−6,2π/3), (−3,π/3), and (-4, π/4).
To find three additional polar coordinate pairs for the point B (-3, 2π/3), we can vary the radius and the angle within the given range of -2 < π < 2. Here are three additional pairs:
1. (-3, π/3): Here, we decrease the angle by π/3 (120 degrees) while keeping the radius (-3) the same.
2. (3, -π/3): Now, we change the radius to its absolute value (3) and negate the angle to get the opposite direction. In this case, the angle becomes -π/3 (-120 degrees).
3. (3, -5π/3): For the third pair, we increase the angle beyond the given range by adding 2π to it. So, we have -2π/3 + 2π = -4π/3. Then, we take the absolute value of the radius (3) and the final pair is (3, -5π/3) or approximately (3, -3.93).
Note: In polar coordinates, the angle is measured counterclockwise from the positive x-axis, and the radius denotes the distance from the origin.