Which of the following is another representation of the polar coordinate P=3,45° ?
yes
To determine another representation of the polar coordinate P = 3, 45°, we can use the conversion formulas between polar and rectangular coordinates. Polar coordinates consist of a distance (r) from the origin and an angle (θ) in degrees or radians.
The conversion formulas between polar and rectangular coordinates are:
x = r * cos(θ)
y = r * sin(θ)
Given that P = 3, 45°, we have r = 3 and θ = 45°.
To find the rectangular coordinates (x, y), we substitute r and θ into the conversion formulas:
x = 3 * cos(45°)
y = 3 * sin(45°)
Using a calculator:
x = 3 * cos(45°) ≈ 2.12
y = 3 * sin(45°) ≈ 2.12
Therefore, another representation of the polar coordinate P = 3, 45° in rectangular coordinates is approximately (2.12, 2.12).