Module 1: Practice Problems
Angles and Their Measure
Instructions: Work through each problem on your own before revealing the solution. These problems cover all four lessons in Module 1.
1 Classifying Angles
Classify each angle: (a) 52° (b) 98° (c) 180° (d) 275° (e) 90°
Solution
(a) Acute (0°<52°<90°) (b) Obtuse (90°<98°<180°) (c) Straight (d) Reflex (180°<275°<360°) (e) Right
2 Coterminal Angles
Find one positive and one negative angle coterminal with 160°.
Solution
Positive: 160° + 360° = 520°. Negative: 160° − 360° = −200°.
3 Complement and Supplement
Find the complement and supplement of 73°.
Solution
Complement: 90° − 73° = 17°. Supplement: 180° − 73° = 107°.
4 Degree-Radian Conversion
Convert 315° to radians.
Solution
315 × π/180 = 315π/180 = 7π/4
5 Radian-Degree Conversion
Convert 5π/6 to degrees.
Solution
(5π/6) × (180/π) = 5(180)/6 = 900/6 = 150°
6 Arc Length
Find the arc length intercepted by a central angle of 2π/3 radians in a circle of radius 9 cm.
Solution
s = rθ = 9(2π/3) = 18π/3 = 6π ≈ 18.85 cm
7 Sector Area
Find the area of a sector with radius 10 m and central angle 45°.
Solution
Convert: 45° = π/4. A = (1/2)(10)²(π/4) = (1/2)(100)(π/4) = 100π/8 = 25π/2 ≈ 39.27 m²
8 Finding the Radius
A sector has an area of 24π ft² and a central angle of π/3. Find the radius.
Solution
A = (1/2)r²θ ⇒ 24π = (1/2)r²(π/3) = πr²/6. So r² = 144, r = 12 ft.
9 Angular Speed
A Ferris wheel makes 3 revolutions per minute. Find the angular speed in rad/s.
Solution
ω = 3 × 2π / 60 = 6π/60 = π/10 ≈ 0.314 rad/s
10 Linear Speed
A wheel of radius 2 feet rotates at 100 rpm. Find the linear speed of a point on the rim in ft/s.
Solution
ω = 100 × 2π = 200π rad/min. v = rω = 2(200π) = 400π ft/min. Convert: 400π/60 = 20π/3 ≈ 20.94 ft/s