Module 1 Quiz: Angles and Their Measure
Test Your Knowledge
Answer each question, then reveal the answer to check your work. Aim for at least 7 out of 10 correct!
1
What type of angle measures exactly 180°?
Straight angle. A 180° angle forms a straight line.
2
Find the smallest positive coterminal angle for −85°.
275°. −85° + 360° = 275°.
3
Convert 240° to radians.
4π/3. 240 × π/180 = 240π/180 = 4π/3.
4
Convert 11π/6 radians to degrees.
330°. (11π/6)(180/π) = 11(180)/6 = 1980/6 = 330.
5
Find the complement of 27°.
63°. 90° − 27° = 63°.
6
Find the arc length on a circle of radius 14 cm with a central angle of π/7.
2π ≈ 6.28 cm. s = rθ = 14(π/7) = 2π.
7
Find the area of a sector with radius 6 in. and central angle 120°.
12π ≈ 37.70 in². Convert: 120° = 2π/3. A = (1/2)(36)(2π/3) = 12π.
8
A wheel makes 60 rpm. What is its angular speed in rad/s?
2π ≈ 6.28 rad/s. ω = 60 × 2π / 60 = 2π.
9
A wheel of radius 4 ft has angular speed 3π rad/s. Find the linear speed of a point on the rim.
12π ≈ 37.70 ft/s. v = rω = 4(3π) = 12π.
10
In which quadrant does the terminal side of 5π/4 lie?
Quadrant III. 5π/4 = 225°, and 180° < 225° < 270°.