Are 22pi/5 and 100 degrees coterminal? explain.
22/5 = 4 2/5
so twice around and then 2 pi/5 in quadrant 1
100 degrees is not in quadrant 1
To determine if two angles, 22π/5 and 100 degrees, are coterminal, we need to check if they end at the same position on the unit circle.
First, let's convert 100 degrees to radians. One complete revolution is equal to 2π radians, so we divide 100 by 360 and multiply by 2π to convert degrees to radians.
100 degrees * (2π radians/360 degrees) = (10π/9) radians
Now, let's compare the two angles: 22π/5 and 10π/9 radians. We can simplify them by multiplying both angles by their common denominators.
22π/5 = (22/5)(π/1) = 44π/10
10π/9 = (10/9)(π/1) = 10π/9
As we can see, 44π/10 and 10π/9 radians are not the same. Therefore, the angles 22π/5 and 100 degrees are not coterminal.
In general, two angles are coterminal if they have the same initial and terminal sides on the unit circle. To find coterminal angles, we can add or subtract multiple full revolutions (2π) or fractions of a revolution (2π k, where k is an integer).