Angles

Correct answer: C. (\frac{9\pi}{2})

(2.25=\frac{9}{4}) revolutions, so the angle is (\frac{9}{4}\times2\pi=\frac{9\pi}{2}). In exams, multiply revolutions by (2\pi).

Correct answer: A. (57^\circ 18')

(1) radian is approximately (57.2958^\circ), which is close to (57^\circ 18'). In exams, multiply the decimal part by (60).

Correct answer: B. (\frac{\theta-\phi}{2\pi})

The difference of coterminal angles is (2\pi n), so (\frac{\theta-\phi}{2\pi}) is an integer. In exams, check the difference, not the sum.

Correct answer: D. (90^\circ)

Since (a-b=4b) must be a multiple of (360^\circ), the least (b=90^\circ). In exams, apply the coterminal condition to the difference.

Correct answer: A. First quadrant and (45^\circ)

(765^\circ-720^\circ=45^\circ), which lies in the first quadrant. In exams, first find the coterminal angle and then the reference angle.

Correct answer: C. (80^\circ)

(-1000^\circ+1080^\circ=80^\circ). In exams, add multiples of (360^\circ) to a large negative angle.

Correct answer: B. (\frac{5\pi}{12})

The first angle gives (\frac{\pi}{4}) and the second gives (\frac{\pi}{6}), so the sum is (\frac{5\pi}{12}). In exams, reduce both angles separately.

Correct answer: D. (50^\circ)

(\frac{7\pi}{18}=70^\circ), so the original angle is (70^\circ-20^\circ=50^\circ). In exams, first convert the final measure into degrees.

Correct answer: A. (\frac{119\pi}{720})

(30^\circ-15'=29^\circ45'=\frac{119}{4}^\circ), so the radian measure is (\frac{119\pi}{720}). In exams, convert minutes into a fraction of a degree.