Angles and Radian Measure — Trigonometry Unit 1 practice.
This unit covers degree to radian conversion, coterminal angles and arc length and sector area — essential concepts for Trigonometry. Use our interactive study games to test your understanding, or review questions in traditional format below.
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This unit covers degree to radian conversion, coterminal angles and arc length and sector area — essential concepts for Trigonometry. Use our interactive study games to test your understanding, or review questions in traditional format below.
Key Concepts Breakdown
1 Degree To Radian Conversion
Degrees and radians are two units for measuring angles, and you must be able to convert fluently between them. The conversion factor is π radians = 180°. Multiply by π/180 to convert degrees to radians, and by 180/π to convert radians to degrees.
Key Points
- π radians = 180°; this is the foundation of all conversions
- Degrees → Radians: multiply by π/180
- Radians → Degrees: multiply by 180/π
- Memorize common angles: 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2, 180° = π, 270° = 3π/2, 360° = 2π
Convert 135° to radians.
Multiply 135 by π/180 to get 135π/180. Simplify by dividing numerator and denominator by their GCF of 45, giving 3π/4. The answer is 3π/4 radians.
2 Coterminal Angles
Coterminal angles share the same terminal side when drawn in standard position, and they differ by full rotations of 360° (or 2π radians). Exams ask you to find positive and negative coterminal angles, or to determine if two given angles are coterminal.
Key Points
- Add or subtract 360° (or 2π) any number of times to find coterminal angles
- Every angle has infinitely many coterminal angles
- To find the smallest positive coterminal angle, keep adding 360° until the result is between 0° and 360°
- Two angles are coterminal if their difference is a multiple of 360° (or 2π)
Find one positive and one negative coterminal angle for 50°.
Add 360° to get the positive coterminal angle: 50° + 360° = 410°. Subtract 360° to get the negative coterminal angle: 50° − 360° = −310°. Both 410° and −310° are coterminal with 50° because they all share the same terminal side.
3 Arc Length And Sector Area
Arc length and sector area formulas use radian measure, so the central angle must always be in radians before applying them. Arc length is s = rθ and sector area is A = ½r²θ, where r is radius and θ is the central angle in radians.
Key Points
- Arc length formula: s = rθ (θ must be in radians)
- Sector area formula: A = ½r²θ (θ must be in radians)
- If the angle is given in degrees, convert to radians first before substituting
- Arc length is a distance (units of length); sector area is in square units
A circle has radius 6 cm. Find the arc length and sector area for a central angle of 120°.
First convert 120° to radians: 120 × π/180 = 2π/3. Then apply the arc length formula: s = 6 × 2π/3 = 4π ≈ 12.57 cm. For sector area: A = ½ × 6² × 2π/3 = ½ × 36 × 2π/3 = 12π ≈ 37.70 cm².
Questions, answered.
What is Angles and Radian Measure?
Angles and Radian Measure is Unit 1 of Trigonometry, covering degree to radian conversion, coterminal angles and arc length and sector area.
How to study for Trigonometry Unit 1?
Start with the Quick Summary above, review the Key Concepts, then test yourself with our interactive study games. Aim for 80%+ accuracy before moving on.
How many questions are in this unit?
This unit has 25+ review questions across 5 different game modes.