Given: Circle O with radius of length 4 units. measurement of arc PQ=141 degrees. Find the cordinates of point P. Circle O(0,0)
To find the coordinates of point P on a circle with radius 4 units and center O(0,0), we need to use trigonometry.
1. First, let's find the angle in radians for the arc PQ. Since there are 360 degrees in a full circle, we can convert 141 degrees to radians by using the formula:
angle in radians = (angle in degrees) * (π / 180)
Plugging in the given value, we have:
angle in radians = 141 * (π / 180)
≈ 2.464 radians
2. Next, we can use trigonometry to find the coordinates of point P. Since the center of the circle is at (0,0), we can use the formula:
x = radius * cos(angle)
y = radius * sin(angle)
Plugging in the values, we have:
x = 4 * cos(2.464)
y = 4 * sin(2.464)
Calculating these values, we find:
x ≈ 2.285
y ≈ 2.815
Therefore, the coordinates of point P are approximately (2.285, 2.815).