The number of revolutions made by a figure skater for each type of axel jump is given. Determine the measure of the angle generated as the skater performs each jump. Give the answer in both degrees and radians.
a. single axel: 1.5
b. double axel: 2.5
c. triple axel: 3.5
For radians, multiply the number of jump revolutions by 2 pi
For degrees, multiply the number of revolutions by 360
To determine the measure of the angle generated as the skater performs each jump, we need to calculate the number of revolutions made by the skater and then convert it to degrees and radians.
1. Single axel: The skater makes 1.5 revolutions.
- To find the measure of the angle, we multiply the number of revolutions by 360 degrees:
1.5 revolutions * 360 degrees/revolution = 540 degrees.
- To convert the measure to radians, we use the fact that π radians = 180 degrees:
540 degrees * (π radians/180 degrees) ≈ 9.42478 radians.
Therefore, the angle generated during a single axel jump is approximately 540 degrees (in degrees) or approximately 9.42478 radians (in radians).
2. Double axel: The skater makes 2.5 revolutions.
- Using the same method as above, we find:
2.5 revolutions * 360 degrees/revolution = 900 degrees.
- To convert to radians:
900 degrees * (π radians/180 degrees) ≈ 15.70796 radians.
So, the angle generated during a double axel jump is approximately 900 degrees (in degrees) or approximately 15.70796 radians (in radians).
3. Triple axel: The skater makes 3.5 revolutions.
- Again, applying the calculation, we get:
3.5 revolutions * 360 degrees/revolution = 1260 degrees.
- To convert to radians:
1260 degrees * (π radians/180 degrees) ≈ 21.99115 radians.
Hence, the angle generated during a triple axel jump is approximately 1260 degrees (in degrees) or approximately 21.99115 radians (in radians).
To determine the measure of the angle generated as the skater performs each jump, we need to relate the number of revolutions made to the angle measure.
The angle formed in a full revolution is 360 degrees or 2π radians. So, if we divide the number of revolutions by the total number of revolutions in a full circle, we can find the angle measure.
Let's calculate the angle measure for each jump:
a. Single Axel: The skater completes 1.5 revolutions.
Angle measure in degrees = 1.5 * 360 = 540 degrees
Angle measure in radians = 1.5 * 2π = 3π radians
b. Double Axel: The skater completes 2.5 revolutions.
Angle measure in degrees = 2.5 * 360 = 900 degrees
Angle measure in radians = 2.5 * 2π = 5π radians
c. Triple Axel: The skater completes 3.5 revolutions.
Angle measure in degrees = 3.5 * 360 = 1260 degrees
Angle measure in radians = 3.5 * 2π = 7π radians
Therefore, the measures of the angles generated in each jump are:
a. Single Axel: 540 degrees (3π radians)
b. Double Axel: 900 degrees (5π radians)
c. Triple Axel: 1260 degrees (7π radians)