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Quizzes > High School Quizzes > Mathematics

Degrees and Radians Conversion Practice Quiz

Boost your confidence with conversion practice questions

Difficulty: Moderate
Grade: Grade 10
Study OutcomesCheat Sheet
Colorful paper art promoting Degrees Radians Rumble, a math practice quiz for high school students.

What is 0° in radians?
0
2π
π
π/2
0° converted to radians is 0 because multiplying by π/180 yields 0. This is the most basic conversion in angle measurement.
Convert 90° to radians.
π/4
π
π/2
π/3
Multiplying 90° by π/180 gives π/2 radians. This conversion is a common step in trigonometric calculations.
Convert 180° to radians.
0
π
π/2
2π
180° multiplied by π/180 simplifies directly to π radians. This conversion is fundamental when transitioning between degree and radian measures.
Convert 360° to radians.
π/2
π
4π
2π
360° converts to 2π radians because 360 multiplied by π/180 equals 2π. This represents one complete revolution around a circle.
Approximately how many degrees are in 1 radian?
60°
180°
45°
57.3°
One radian is approximately 57.3° because the conversion factor 180/π is roughly 57.3. This approximation is very useful in various math and physics problems.
Convert π/3 radians to degrees.
30°
45°
90°
60°
Multiplying π/3 by 180/π gives 60°, establishing the equivalence between radians and degrees. This conversion is essential when comparing different angle measures.
Convert 270° to radians.
π
2π
3π/2
4π/3
To convert 270° into radians, multiply 270 by π/180 to obtain 3π/2. This conversion is frequently used in trigonometric and circular motion problems.
Convert 45° to radians.
π/4
π/6
π/3
π/2
Multiplying 45° by π/180 results in π/4 radians. This conversion is a staple in both geometry and trigonometry.
Which angle in degrees is equivalent to 3π/4 radians?
120°
135°
150°
90°
Multiplying 3π/4 by 180/π gives 135°, which is the correct degree measure. Understanding this conversion reinforces the relationship between radian and degree angles.
Convert 225° to radians.
3π/4
π/4
5π/4
7π/4
Multiplying 225° by π/180 yields 5π/4 radians. This conversion is important when working with angles in multiple quadrants.
Convert 7π/6 radians to degrees.
210°
150°
120°
180°
Multiplying 7π/6 by 180/π converts the measure to 210°. This calculation illustrates the seamless conversion between radian and degree systems.
What is the radian measure of 30°?
π/2
π/3
π/4
π/6
Multiplying 30° by π/180 gives π/6 radians. This conversion is commonly used in problems involving small angle approximations.
Convert 120° to radians.
π/2
π/3
3π/4
2π/3
Multiplying 120° by π/180 results in 2π/3 radians. This conversion is useful in various trigonometric applications.
Which of the following is the correct conversion of 2π/3 radians to degrees?
120°
90°
60°
150°
Multiplying 2π/3 by 180/π converts it to 120°. This demonstrates the inverse process of degree-to-radian conversion.
An angle measures 2 radians. What is its approximate measure in degrees?
114.6°
110°
120°
100°
Multiplying 2 radians by 180/π yields approximately 114.6°. This conversion helps in visualizing radian measures in a degree context.
Find the radian measure equivalent to a rotation of 450°.
3π/2
π
2π
π/2
A 450° rotation exceeds a full circle; subtracting 360° gives 90°. Converting 90° to radians results in π/2, making it the correct answer.
Convert 1.2 radians to degrees (approximate).
60.0°
68.8°
70.0°
72.0°
Multiplying 1.2 by 180/π gives an approximate value of 68.8°. This conversion is crucial when precise degree measures are needed from radian values.
Find the difference in radian measure between 150° and 45°.
π/3
7π/12
5π/12
π/2
Subtracting 45° from 150° gives 105°, and converting 105° by multiplying with π/180 yields 7π/12. This problem tests both subtraction of angles and the conversion process.
A circle's arc length formula is s = rθ. If the central angle is 135°, what is θ in radians?
π/2
π/3
2π/3
3π/4
For the arc length formula, the angle must be in radians. Converting 135° to radians by multiplying by π/180 produces 3π/4, which is the required value for θ.
Which one of the following radian measures is equivalent to 330°?
7π/6
3π/2
5π/3
11π/6
Converting 330° to radians by multiplying with π/180 gives 11π/6. This conversion confirms the equivalence between the two measurement systems, validating the correct answer.
0
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Study Outcomes

  1. Apply conversion formulas to accurately switch between degree and radian measures.
  2. Analyze angle measurements to determine the appropriate conversion method.
  3. Synthesize problem-solving strategies for effective angle conversion in diverse math scenarios.
  4. Evaluate conversion results to ensure precision in trigonometric applications.

Degrees & Radians Conversion Practice Cheat Sheet

  1. 180° = π Radians - This golden rule unlocks the magic of angle conversion, showing that a straight line spans 180° or π radians. Once you memorize this, you can effortlessly switch between the two measurement systems without breaking a sweat. For example, 90° instantly becomes π/2 radians like math sorcery! Byju's Degrees to Radians
  2. Multiply by π/180 for Degrees → Radians - To convert any angle from degrees to radians, just multiply by π/180 and watch the number transform. For instance, 45° × π/180 gives π/4 radians, making your trigonometry homework feel like a breeze. This simple trick is a must-know for all your angle adventures! GeeksforGeeks: Degrees to Radians
  3. Multiply by 180/π for Radians → Degrees - Flipping back from radians is just as easy: multiply by 180/π to reveal the degree measure. For example, π/3 × 180/π = 60°, turning abstract radians into a familiar degree value in seconds. It's like hitting rewind on your conversions! GeeksforGeeks: Radians to Degrees
  4. Memorize Key Angles - Keep the classic quartet in your brain: 30° = π/6, 45° = π/4, 60° = π/3, and 90° = π/2 radians. These go-to angles pop up constantly in trigonometry, so knowing them by heart saves you precious time. Think of it as your personal angle flash card deck! RapidTables Angle Converter
  5. Full Circle Fact - A full rotation measures 360° or 2π radians, revealing the cyclical nature of circles and waves. This concept is the backbone of understanding periodic functions, from sine waves to planetary orbits. Embrace it and you'll never spin out of trigonometry again! Math.net Radians & Degrees
  6. Handle Negative Angles - Negative angles simply mean a clockwise turn, and you convert them the same way: multiply by π/180. For example, - 45° × π/180 = - π/4 radians, giving you a smooth rotation into negative territory. It's a neat way to explore clockwise spins without losing your cool! Byju's Negative Angle Guide
  7. Use the Unit Circle - Picture angles on the unit circle to link degrees and radians with coordinates (x, y) at each point. This visual tool cements your understanding of trig functions and angle measures in both systems. Soon you'll navigate the circle like a pro explorer! ChiliMath Unit Circle Lesson
  8. Why Radians Rock - Radians are the superstar in calculus and physics because they simplify derivatives and integrals of trig functions. Using radians turns messy formulas into sleek expressions, making advanced math feel more approachable. Once you switch, you'll never look back! GeeksforGeeks on Radians
  9. Convert DMS to Radians - For angles in degrees, minutes, and seconds, first turn everything into decimal degrees (e.g., 30°15′ = 30.25°). Then apply the π/180 rule: 30.25° × π/180 ≈ 0.527 radians. This two-step process tackles even the trickiest angle formats! GeeksforGeeks DMS Conversion
  10. Check with Online Tools - Want instant feedback? Use reliable calculators to verify your manual conversions and build confidence. Consistent practice and cross‑checking keep mistakes at bay and sharpen your skills. Soon you'll convert angles in your sleep! RapidTables Conversion Tool
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