Question 4.1.6: Finding Coterminal Angles Assume the following angles are in...
Finding Coterminal Angles Assume the following angles are in standard position. Find a positive angle less than 2π that is coterminal with each of the following:
a. a \frac{17 \pi}{6} angle b. a -\frac{\pi}{12} angle.
We obtain the coterminal angle by adding or subtracting 2π. The requirement to obtain a positive angle less than 2π determines whether we should add or subtract.
a. For a \frac{17 \pi}{6} angle, note that \frac{17}{6}=2 \frac{5}{6}, so subtract 2π to find a positive coterminal angle.
\frac{17 \pi}{6}-2 \pi=\frac{17 \pi}{6}-\frac{12 \pi}{6}=\frac{5 \pi}{6}
A \frac{5 \pi}{6} angle is coterminal with a \frac{17 \pi}{6} angle. Figure 4.17(a) illustrates that these angles have the same initial and terminal sides.
b. For a -\frac{\pi}{12} angle, add 2π to find a positive coterminal angle.
A \frac{23 \pi}{12} angle is coterminal with a -\frac{\pi}{12} angle. Figure 4.17(b) illustrates that these angles have the same initial and terminal sides.
