Find an angle between 0 degree and 360 degree that is coterminal with given angle.
a. 361 degree
b. -100 degree
c. 1270 degree
To find the coterminal angle, you can subtract or add 360° until the angle is between 0 and 360°.
For example, 361° is more than 360° so we subtract 360° to get 1°. Since 1° is between 0 and 360°, it is the coterminal angle with 361°.
You can apply the same method for the other two questoins.
The smallest positive angle that is coterminal with negative StartFraction 5 pi Over 7 EndFraction
To find an angle that is coterminal with a given angle, we need to add or subtract multiples of 360 degrees.
a. For 361 degrees:
Since 361 degrees is 1 degree more than 360 degrees, we can subtract 360 degrees from it to find the coterminal angle:
361 degrees - 360 degrees = 1 degree
Therefore, an angle coterminal with 361 degrees is 1 degree.
b. For -100 degrees:
Since -100 degrees is negative, we need to add multiples of 360 degrees to find a positive coterminal angle.
We can add 360 degrees to -100 degrees to find the coterminal angle:
-100 degrees + 360 degrees = 260 degrees
Therefore, an angle coterminal with -100 degrees is 260 degrees.
c. For 1270 degrees:
Since 1270 degrees is greater than 360 degrees, we need to subtract multiples of 360 degrees to find the smallest positive coterminal angle.
We can subtract 360 degrees from 1270 degrees multiple times until we get an angle between 0 and 360 degrees:
1270 degrees - 360 degrees = 910 degrees (still greater than 360 degrees)
910 degrees - 360 degrees = 550 degrees (still greater than 360 degrees)
550 degrees - 360 degrees = 190 degrees (between 0 and 360 degrees)
Therefore, an angle coterminal with 1270 degrees is 190 degrees.
To find an angle that is coterminal with a given angle, you need to add or subtract a multiple of 360 degrees.
a. For the angle 361 degrees, we can subtract multiples of 360 degrees until we get an angle between 0 and 360 degrees:
361 degrees - (1 * 360 degrees) = 1 degree
So, the angle 1 degree is coterminal with 361 degrees.
b. For the angle -100 degrees, we can add multiples of 360 degrees until we get an angle between 0 and 360 degrees:
-100 degrees + (1 * 360 degrees) = 260 degrees
So, the angle 260 degrees is coterminal with -100 degrees.
c. For the angle 1270 degrees, we can subtract multiples of 360 degrees until we get an angle between 0 and 360 degrees:
1270 degrees - (3 * 360 degrees) = 190 degrees
So, the angle 190 degrees is coterminal with 1270 degrees.
Therefore, the angles coterminal with the given angles are:
a. 1 degree
b. 260 degrees
c. 190 degrees