Question 4.1.7: Finding Coterminal Angles Find a positive angle less than 36...

a. For a 750° angle, subtract two multiples of 360°, or 720°, to find a positive coterminal angle less than 360°.

750° – 360° · 2 = 750° – 720° = 30°

A 30° angle is coterminal with a 750° angle.

b. For a \frac{22 \pi}{3} angle, note that \frac{22}{3}=7 \frac{1}{3}, so subtract three multiples of 2π, or 6π, to find a positive coterminal angle less than 2π.

\frac{22 \pi}{3}-2 \pi \cdot 3=\frac{22 \pi}{3}-6 \pi=\frac{22 \pi}{3}-\frac{18 \pi}{3}=\frac{4 \pi}{3}

A \frac{4 \pi}{3} angle is coterminal with a \frac{22 \pi}{3} angle.

c. For a -\frac{17 \pi}{6} angle, note that -\frac{17}{6}=-2 \frac{5}{6}, so add two multiples of 2π, or 4π, to find a positive coterminal angle less than 2π.

-\frac{17 \pi}{6}+2 \pi \cdot 2=-\frac{17 \pi}{6}+4 \pi=-\frac{17 \pi}{6}+\frac{24 \pi}{6}=\frac{7 \pi}{6}

A \frac{7 \pi}{6} angle is coterminal with a -\frac{17 \pi}{6} angle.

d. For a – 10.3 angle, it is helpful to remember that 1 radian ≈ 57°. Therefore,

–10.3 ≈ –10.3(57°) = –587.1°.

For a -587.1° angle, we need to add two multiplies of 360° to find a positive coterminal angle less than 360°. Equivalently, for a – 10.3 angle, we need to add two multiples of 2π, or 4π, to find a positive coterminal angle less than 2π.

–10.3 + 2π · 2 = –10.3 + 4π ≈ 2.3

A 2.3 angle is approximately coterminal with a –10.3 angle.