07.6 - Radians on the Unit Circle

Convert the angle θ = 135° from degrees to radian measure or radians to degrees, whichever is appropriate. Fill in the blank with the correct answer.

• θ = 3π/4

• θ = 5π/6

• θ = 2π/3

• θ = π/2

Answer explanation

To convert 135° to radians, use the formula: radians = degrees × (π/180). Thus, 135° × (π/180) = 3π/4. Therefore, the correct answer is θ = 3π/4.

Convert the angle θ = 240° from degrees to radian measure or radians to degrees, whichever is appropriate. Fill in the blank with the correct answer.

• θ = 4π/3

• θ = 2π/3

• θ = 3π/2

• θ = π/2

Answer explanation

To convert 240° to radians, use the formula: radians = degrees × (π/180). Thus, 240° × (π/180) = 4π/3. Therefore, the correct answer is θ = 4π/3.

Convert the angle θ = 7π/5 from degrees to radian measure or radians to degrees, whichever is appropriate. Fill in the blank with the correct answer.

• θ = 252°

• θ = 180°

• θ = 315°

• θ = 210°

Answer explanation

To convert radians to degrees, use the formula: degrees = radians × (180/π). For θ = 7π/5, it becomes 7π/5 × (180/π) = 252°. Thus, the correct answer is θ = 252°.

Convert the angle θ = 11π/12 from degrees to radian measure or radians to degrees, whichever is appropriate. Fill in the blank with the correct answer.

• θ = 165°

• θ = 150°

• θ = 120°

• θ = 180°

Answer explanation

To convert radians to degrees, use the formula: degrees = radians × (180/π). For θ = 11π/12, it becomes 11π/12 × (180/π) = 165°. Thus, the correct answer is θ = 165°.

Convert the angle θ = 330° from degrees to radian measure or radians to degrees, whichever is appropriate. Fill in the blank with the correct answer.

• θ = 11π/6

• θ = 5π/6

• θ = 7π/4

• θ = 2π/3

Answer explanation

To convert 330° to radians, use the formula θ (radians) = θ (degrees) × π/180. Thus, 330° × π/180 = 11π/6. Therefore, the correct answer is θ = 11π/6.

Convert the angle θ = 270° from degrees to radian measure or radians to degrees, whichever is appropriate. Fill in the blank with the correct answer.

• θ = 3π/2

• θ = π/2

• θ = π

• θ = 2π

Answer explanation

To convert 270° to radians, use the formula: radians = degrees × (π/180). Thus, 270° × (π/180) = 3π/2. Therefore, the correct answer is θ = 3π/2.

Convert the angle θ = 15π/8 from degrees to radian measure or radians to degrees, whichever is appropriate. Fill in the blank with the correct answer.

• θ = 337.5°

• θ = 225°

• θ = 315°

• θ = 270°

Answer explanation

To convert θ = 15π/8 radians to degrees, use the formula: degrees = radians × (180/π). Thus, θ = (15π/8) × (180/π) = 337.5°. Therefore, the correct answer is θ = 337.5°.

Convert the angle θ = 2 from degrees to radian measure or radians to degrees, whichever is appropriate. Fill in the blank with the correct answer.

• θ = 114.6°

• θ = 57.3°

• θ = 1.14°

• θ = 360°

Answer explanation

To convert degrees to radians, use the formula: radians = degrees × (π/180). For θ = 2 degrees, it equals 2 × (π/180) = 0.0349 radians. The correct conversion to degrees is θ = 114.6°, which matches the answer choice.

Convert the angle θ = -3 from degrees to radian measure or radians to degrees, whichever is appropriate. Fill in the blank with the correct answer.

• θ = -171.9°

• θ = -5.24°

• θ = -0.052°

• θ = -34.4°

Answer explanation

To convert -3 radians to degrees, use the formula: degrees = radians × (180/π). Thus, -3 × (180/π) ≈ -171.9°. Therefore, the correct answer is θ = -171.9°.

Convert the angle θ = -315° from degrees to radian measure or radians to degrees, whichever is appropriate. Fill in the blank with the correct answer.

• θ = -7π/4

• θ = -5π/6

• θ = -9π/4

• θ = -11π/6

Answer explanation

To convert -315° to radians, add 360° to get 45°. Then, convert 45° to radians: 45° = π/4. Since the original angle is negative, it becomes -7π/4. Thus, θ = -7π/4 is the correct answer.