The coordinates of the five quarter points for are given below. Use these quarter points to determine the y-coordinates of the quarter points of.
(0,0)
(π/2,1)
(π,0)
(3π/2,-1)
(2π,0)
(Type ordered pairs. Type exact answers, using π as needed)
To determine the y-coordinates of the quarter points, we need to find the average of the y-coordinates of two adjacent points.
Let's start with the first quarter point, which is between (0,0) and (π/2,1). The average of the y-coordinates is (0 + 1)/2 = 1/2. So the y-coordinate of the first quarter point is 1/2.
Now, let's move on to the second quarter point, which is between (π/2,1) and (π,0). Again, we take the average of the y-coordinates: (1 + 0)/2 = 1/2. So the y-coordinate of the second quarter point is also 1/2.
Next, we have the third quarter point, between (π,0) and (3π/2,-1). Average of the y-coordinates: (0 + (-1))/2 = -1/2. Hence, the y-coordinate of the third quarter point is -1/2.
Moving on to the fourth quarter point, between (3π/2,-1) and (2π,0). Average of the y-coordinates: (-1 + 0)/2 = -1/2. So the y-coordinate of the fourth quarter point is -1/2.
Finally, for the fifth quarter point, we need to take the average between (2π,0) and (0,0) since it's the last quarter of the coordinates. The y-coordinate will be the average of 0 and 0, which is 0.
Therefore, the coordinates of the quarter points are:
First quarter point: (π/2, 1/2)
Second quarter point: (π, 1/2)
Third quarter point: (3π/2, -1/2)
Fourth quarter point: (2π, -1/2)
Fifth quarter point: (0, 0)