Find an angle between 0 and 2Ð that is coterminal with given angle.
1. -7Ð /3
2. 10
3. 51Ð /2
The same applies as with angles measured in degrees.
Add or subtract 2π until the angle is between 0 and 2π.
1)
Since the angle is negative, we add 2π
-7π/3 + 2π =-π/3
The result is still negative, so we add 2π again to get
-&pi/3 + 2π = 5π/3
Since 0 ≤ 5π/3 ≤ 2π
5π/3 is coterminal with -7π/3.
For 2 and 3, proceed the same way.
To find a coterminal angle, we need to add or subtract a multiple of 2π (or 360°) to the given angle. This will result in an angle that has the same initial and terminal sides as the given angle.
Let's find the coterminal angles for each given angle:
1. For -7π/3:
Adding 2π, we get: (-7π/3) + 2π = -7π/3 + 6π/3 = -π/3
Adding another 2π, we get: -π/3 + 2π = 5π/3
Therefore, the angle -7π/3 has two coterminal angles: -π/3 and 5π/3.
2. For 10:
Since no units are given, we'll assume it's in degrees.
Adding 360°, we get: 10° + 360° = 370°
Adding another 360°, we get: 370° + 360° = 730°
Therefore, the angle 10° has two coterminal angles: 370° and 730°.
3. For 51π/2:
Adding 2π, we get: (51π/2) + 2π = 51π/2 + 4π/2 = 55π/2
Adding another 2π, we get: 55π/2 + 2π = 59π/2
Therefore, the angle 51π/2 has two coterminal angles: 55π/2 and 59π/2.
In summary:
1. The coterminal angles for -7π/3 are -π/3 and 5π/3.
2. The coterminal angles for 10° are 370° and 730°.
3. The coterminal angles for 51π/2 are 55π/2 and 59π/2.