Convert the following polar coordinates to rectangular coordinates. (-3, 240°)Give your answer in the form: (x,y) where "x" and "y" are rounded to the nearest tenths
Question
Convert the following polar coordinates to rectangular coordinates. (-3, 240°)Give your answer in the form: (x,y) where "x" and "y" are rounded to the nearest tenths
Solution
To convert polar coordinates to rectangular coordinates, we use the following formulas:
x = rcos(θ) y = rsin(θ)
Given the polar coordinates (-3, 240°), we can substitute these values into the formulas.
First, convert the angle from degrees to radians because the trigonometric functions in most programming languages use radians, not degrees.
240° = 240 * π/180 = 4π/3 radians
Now, substitute r = -3 and θ = 4π/3 into the formulas:
x = -3cos(4π/3) = 1.5 y = -3sin(4π/3) = -2.6
So, the rectangular coordinates are approximately (1.5, -2.6).
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