Convert ( 4, -pi/6) from polar coordinates to rectangular coordinates. I got sqrt 12, -2 as my answer but it said this was wrong. I checked multiple times and I don't see where I messed up
Never mind I got it
To convert polar coordinates to rectangular coordinates, you can use the following equations:
x = r * cos(theta)
y = r * sin(theta)
Here, (r, theta) represents the polar coordinates, where r is the distance from the origin and theta is the angle in radians.
Let's apply these equations to the given polar coordinates (4, -pi/6):
x = 4 * cos(-pi/6)
y = 4 * sin(-pi/6)
Now, let's evaluate these equations:
x = 4 * cos(-pi/6)
≈ 4 * (sqrt(3)/2)
≈ 4 * 0.86602540378
≈ 3.46410161514
y = 4 * sin(-pi/6)
≈ 4 * (-1/2)
≈ -2
So, the rectangular coordinates for (4, -pi/6) are approximately (3.4641, -2).
Please note that your answer, sqrt(12), -2, is mathematically equivalent to 3.4641, -2. There seems to be an error with how you formatted your answer. However, please double-check your calculations to ensure accuracy.