What is the measure of a counterclockwise rotation about the spinner center that maps label i to label f?
To determine the measure of a counterclockwise rotation about the spinner center that maps label i to label f, we need to use the positions of the labels on the spinner.
Since the clockwise rotation is usually measured as positive, we will measure the counterclockwise rotation as negative.
Assuming a spinner with labels i and f, we can determine the measure of counterclockwise rotation by starting from i and counting the number of positions in the counterclockwise direction until we reach f. Each position will be counted as a negative rotation.
For example, if label i is at position 1 and label f is at position 6 on the spinner, we count 5 positions counterclockwise from i to f. Therefore, the measure of this counterclockwise rotation is -5.
In general, the measure of a counterclockwise rotation from i to f can be calculated as (-1) multiplied by the number of positions counted counterclockwise from i to f on the spinner.
108 degrees
72 degrees
36 degrees
252 degrees
To determine the measure of a counterclockwise rotation about the spinner center that maps label i to label f, we need to make use of modulo arithmetic.
Firstly, we need to establish a reference point. Let's assume that label i is at position 0 on the spinner. In this case, to find the counterclockwise rotation that maps label i to label f, we need to find the position of label f when starting from position 0.
1. 108 degrees:
If the counterclockwise rotation from i to f is 108 degrees, it means that label f is 108 degrees counterclockwise from starting position 0.
Since one complete revolution is 360 degrees, we can use modulo arithmetic to find the equivalent position within a single revolution:
108 degrees % 360 degrees = 108 degrees
Therefore, the measure of the counterclockwise rotation from i to f is 108 degrees.
2. 72 degrees:
Using the same modulo arithmetic, we can calculate the position of label f when starting from position 0:
72 degrees % 360 degrees = 72 degrees
Therefore, the measure of the counterclockwise rotation from i to f is 72 degrees.
3. 36 degrees:
Calculating the position of label f when starting from position 0:
36 degrees % 360 degrees = 36 degrees
Therefore, the measure of the counterclockwise rotation from i to f is 36 degrees.
4. 252 degrees:
Calculating the position of label f when starting from position 0:
252 degrees % 360 degrees = 252 degrees
Therefore, the measure of the counterclockwise rotation from i to f is 252 degrees.