Find the rectangular coordinates of the point with the given polar coordinates. (3, 150°)
r cos theta = x = -2.598 = - 3(sqrt3/2)
r sin theta = y = +1.5
(-2.6 , 1.5 )
or exact:
(-3 sqrt 3 /2 , 3/2 )
To find the rectangular coordinates of a point given polar coordinates, we can use the following formulas:
x = r * cos(θ)
y = r * sin(θ)
In this case, the given polar coordinates are (3, 150°).
First, let's substitute the values into the formulas:
x = 3 * cos(150°)
y = 3 * sin(150°)
Next, we need to calculate the cosine and sine of 150°. However, most calculators use radians instead of degrees, so we need to convert 150° to radians.
To convert degrees to radians, we can use the formula:
radians = degrees * π / 180
Let's calculate the radians:
radians = 150° * π / 180
Now, let's calculate the cosine and sine of 150° in radians:
cos(150°) ≈ cos(radians)
sin(150°) ≈ sin(radians)
Finally, we can substitute the approximate values of the cosine and sine into the formulas:
x ≈ 3 * cos(radians)
y ≈ 3 * sin(radians)
Calculating the approximate values with a calculator or a programming language will give you the rectangular coordinates of the point with polar coordinates (3, 150°).