A point in polar coordinates is given, Find the corresponding rectangular coordinates for the point.
(r,Q) = (4, 3pi/2)
I know that you are suppose to use
x=r cos Q and y=sin Q but I do not know how to plug this in.
3 pi/2 is straight down the y axis
x = 4 cos (3pi/2)
but cos 3pi/2 is 0
so x = 0
sin 3pi/2 = -1
so y = -4
so (0,-4)
if (r,Q) = (4, 3pi/2)
then r = 4 and Q = 3π/3
now just substitute ...
x = 4cos 3π/2 and y = 4sin 3π/2
x = 0 and y = 4(-1) = -4
so the point is (0,-4)
To find the corresponding rectangular coordinates (x, y) for a point given in polar coordinates (r, θ), you can use the formulas x = r * cos(θ) and y = r * sin(θ).
In this case, you're given (r, θ) = (4, 3π/2). To find the rectangular coordinates (x, y), you plug in the values into the formulas:
x = r * cos(θ)
x = 4 * cos(3π/2)
First, calculate cos(3π/2). The cosine of (3π/2) is 0.
x = 4 * 0
x = 0
So the x-coordinate is 0.
Now, let's find the y-coordinate:
y = r * sin(θ)
y = 4 * sin(3π/2)
Similarly, calculate sin(3π/2). The sine of (3π/2) is -1.
y = 4 * (-1)
y = -4
So the y-coordinate is -4.
Therefore, the rectangular coordinates (x, y) for the given polar coordinates (4, 3π/2) are (0, -4).