Quick Answer
SAT radians and degrees practice questions test angle conversion, coterminal angles, reference angles, unit-circle positions, arc length, sector area, special-angle trigonometry, rotations, and real-world circular motion. This guide includes 70 SAT-style questions that progress from basic conversions to arc models, unit-circle reasoning, and harder mixed geometry problems.
What Should You Know Before Practicing Radians and Degrees?
- 180°=π radians.
- 360°=2π radians.
- Convert degrees to radians by multiplying by π/180.
- Convert radians to degrees by multiplying by 180/π.
- Coterminal angles differ by 360° or 2π.
- Arc length is s=rθ when θ is in radians.
- Sector area is (1/2)r²θ when θ is in radians.
- A full rotation equals 360° or 2π radians.
In This Guide – 70 SAT Radians and Degrees Practice Questions
Start With SAT Math Topic-Wise Practice
Connect radians and degrees practice with weekly score planning, mock-test review, and targeted SAT Math correction.
Download the SAT Prep Guide E-Book
Organize radians, degrees, unit-circle practice, and weekly SAT Math preparation with a clear study plan.
Download SAT Prep E-Book GuideWhat Does the SAT Test in Radians and Degrees Questions?
Students may need to convert angle measures, identify coterminal or reference angles, interpret unit-circle positions, calculate arc length or sector area, and model rotations or circular motion.
| Skill Area | What It Tests | Questions |
|---|---|---|
| Conversions | Degrees to radians and radians to degrees | Q1-Q15 |
| Reference and coterminal angles | Quadrants, unit-circle positions, coterminal measures | Q16-Q30 |
| Arc and sector models | Arc length, sector area, angle fractions | Q31-Q45 |
| Advanced applications | Special angles, rotations, clocks, mixed models | Q46-Q70 |
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How Are Degree-Radian Conversions Tested?
These questions focus on exact conversions using 180°=π radians.
DEGREE-RADIAN CONVERSIONS
EASY
Question 1
Convert 180° to radians.
Which choice is correct?
A) π/2
B) π
C) 2π
D) 180π
Show full solution
Correct answer: B) π
Multiply by π/180: 180(π/180)=π.
SAT trap: Use π radians for 180°.
DEGREE-RADIAN CONVERSIONS
EASY
Question 2
Convert 90° to radians.
Which choice is correct?
A) π/6
B) π/4
C) π/2
D) π
Show full solution
Correct answer: C) π/2
90(π/180)=π/2.
SAT trap: Reduce the fraction after multiplying.
DEGREE-RADIAN CONVERSIONS
EASY
Question 3
Convert 60° to radians.
Which choice is correct?
A) π/6
B) π/3
C) π/2
D) 2π/3
Show full solution
Correct answer: B) π/3
60(π/180)=π/3.
SAT trap: Cancel the common factor 60.
DEGREE-RADIAN CONVERSIONS
EASY
Question 4
Convert 45° to radians.
Which choice is correct?
A) π/6
B) π/4
C) π/3
D) π/2
Show full solution
Correct answer: B) π/4
45(π/180)=π/4.
SAT trap: Do not confuse 45° with π/3.
DEGREE-RADIAN CONVERSIONS
EASY
Question 5
Convert 30° to radians.
Which choice is correct?
A) π/6
B) π/4
C) π/3
D) π/2
Show full solution
Correct answer: A) π/6
30(π/180)=π/6.
SAT trap: Use π/180 for degree-to-radian conversion.
DEGREE-RADIAN CONVERSIONS
EASY
Question 6
Convert 270° to radians.
Which choice is correct?
A) 3π/2
B) 2π
C) 5π/3
D) 3π
Show full solution
Correct answer: A) 3π/2
270(π/180)=3π/2.
SAT trap: Reduce 270/180 to 3/2.
DEGREE-RADIAN CONVERSIONS
EASY
Question 7
Convert 360° to radians.
Which choice is correct?
A) π
B) 3π/2
C) 2π
D) 4π
Show full solution
Correct answer: C) 2π
360(π/180)=2π.
SAT trap: A full rotation is 2π radians.
DEGREE-RADIAN CONVERSIONS
EASY
Question 8
Convert 120° to radians.
Which choice is correct?
A) π/3
B) 2π/3
C) 3π/4
D) 5π/6
Show full solution
Correct answer: B) 2π/3
120(π/180)=2π/3.
SAT trap: Reduce 120/180 to 2/3.
DEGREE-RADIAN CONVERSIONS
EASY
Question 9
Convert 150° to radians.
Which choice is correct?
A) 2π/3
B) 3π/4
C) 5π/6
D) 7π/6
Show full solution
Correct answer: C) 5π/6
150(π/180)=5π/6.
SAT trap: Reduce the numerical fraction first.
DEGREE-RADIAN CONVERSIONS
EASY
Question 10
Convert 210° to radians.
Which choice is correct?
A) 5π/6
B) 7π/6
C) 4π/3
D) 3π/2
Show full solution
Correct answer: B) 7π/6
210(π/180)=7π/6.
SAT trap: Angles greater than 180° have radian measures greater than π.
DEGREE-RADIAN CONVERSIONS
MEDIUM
Question 11
Convert π radians to degrees.
Which choice is correct?
A) 90°
B) 120°
C) 180°
D) 360°
Show full solution
Correct answer: C) 180°
Multiply by 180/π: π(180/π)=180°.
SAT trap: Use 180/π for radian-to-degree conversion.
DEGREE-RADIAN CONVERSIONS
MEDIUM
Question 12
Convert π/2 radians to degrees.
Which choice is correct?
A) 30°
B) 45°
C) 60°
D) 90°
Show full solution
Correct answer: D) 90°
(π/2)(180/π)=90°.
SAT trap: Cancel π before multiplying.
DEGREE-RADIAN CONVERSIONS
MEDIUM
Question 13
Convert 2π/3 radians to degrees.
Which choice is correct?
A) 60°
B) 90°
C) 120°
D) 135°
Show full solution
Correct answer: C) 120°
(2π/3)(180/π)=120°.
SAT trap: Multiply the rational coefficient by 180.
DEGREE-RADIAN CONVERSIONS
MEDIUM
Question 14
Convert 5π/4 radians to degrees.
Which choice is correct?
A) 180°
B) 210°
C) 225°
D) 240°
Show full solution
Correct answer: C) 225°
(5π/4)(180/π)=225°.
SAT trap: Divide 180 by 4 before multiplying by 5.
DEGREE-RADIAN CONVERSIONS
MEDIUM
Question 15
Convert 7π/6 radians to degrees.
Which choice is correct?
A) 180°
B) 200°
C) 210°
D) 240°
Show full solution
Correct answer: C) 210°
(7π/6)(180/π)=210°.
SAT trap: Use exact arithmetic rather than decimals.
Build Stronger SAT Angle Skills
Connect degree-radian conversions with unit-circle reasoning and real SAT Math timing.
How Are Coterminal and Reference Angles Tested?
These questions use full rotations, quadrants, reference angles, and unit-circle positions.
COTERMINAL AND REFERENCE ANGLES
MEDIUM
Question 16
Which angle is coterminal with 45°?
Which choice is correct?
A) 135°
B) 225°
C) 405°
D) 495°
Show full solution
Correct answer: C) 405°
Coterminal angles differ by 360°. Since 45+360=405, 405° is coterminal.
SAT trap: Add or subtract whole rotations.
COTERMINAL AND REFERENCE ANGLES
MEDIUM
Question 17
Which angle is coterminal with π/3?
Which choice is correct?
A) 2π/3
B) 4π/3
C) 7π/3
D) 8π/3
Show full solution
Correct answer: C) 7π/3
Add 2π: π/3+2π=7π/3.
SAT trap: A full radian rotation is 2π.
COTERMINAL AND REFERENCE ANGLES
MEDIUM
Question 18
What is the reference angle for 150°?
Which choice is correct?
A) 30°
B) 45°
C) 60°
D) 150°
Show full solution
Correct answer: A) 30°
150° lies in Quadrant II, so the reference angle is 180-150=30°.
SAT trap: Reference angles are acute.
COTERMINAL AND REFERENCE ANGLES
MEDIUM
Question 19
What is the reference angle for 225°?
Which choice is correct?
A) 30°
B) 45°
C) 60°
D) 135°
Show full solution
Correct answer: B) 45°
225° lies in Quadrant III, so the reference angle is 225-180=45°.
SAT trap: Subtract 180° in Quadrant III.
COTERMINAL AND REFERENCE ANGLES
MEDIUM
Question 20
What is the reference angle for 5π/6?
Which choice is correct?
A) π/6
B) π/4
C) π/3
D) 5π/6
Show full solution
Correct answer: A) π/6
5π/6 is in Quadrant II, so π-5π/6=π/6.
SAT trap: Use π as the Quadrant II boundary.
COTERMINAL AND REFERENCE ANGLES
MEDIUM
Question 21
What is the reference angle for 7π/4?
Which choice is correct?
A) π/6
B) π/4
C) π/3
D) 3π/4
Show full solution
Correct answer: B) π/4
7π/4 is in Quadrant IV, so 2π-7π/4=π/4.
SAT trap: Subtract from 2π in Quadrant IV.
COTERMINAL AND REFERENCE ANGLES
MEDIUM
Question 22
In which quadrant does 4π/3 lie?
Which choice is correct?
A) I
B) II
C) III
D) IV
Show full solution
Correct answer: C) III
4π/3=240°, which is in Quadrant III.
SAT trap: Compare the angle with π and 3π/2.
COTERMINAL AND REFERENCE ANGLES
MEDIUM
Question 23
In which quadrant does 11π/6 lie?
Which choice is correct?
A) I
B) II
C) III
D) IV
Show full solution
Correct answer: D) IV
11π/6=330°, which is in Quadrant IV.
SAT trap: Convert to degrees when helpful.
COTERMINAL AND REFERENCE ANGLES
MEDIUM
Question 24
What point on the unit circle corresponds to 0 radians?
Which choice is correct?
A) (0,1)
B) (1,0)
C) (-1,0)
D) (0,-1)
Show full solution
Correct answer: B) (1,0)
At angle 0, the unit-circle point is (cos 0,sin 0)=(1,0).
SAT trap: The positive x-axis is the starting ray.
COTERMINAL AND REFERENCE ANGLES
MEDIUM
Question 25
What point on the unit circle corresponds to π/2?
Which choice is correct?
A) (0,1)
B) (1,0)
C) (-1,0)
D) (0,-1)
Show full solution
Correct answer: A) (0,1)
(cos π/2,sin π/2)=(0,1).
SAT trap: π/2 is the positive y-axis.
COTERMINAL AND REFERENCE ANGLES
HARD
Question 26
What point on the unit circle corresponds to π?
Which choice is correct?
A) (0,1)
B) (1,0)
C) (-1,0)
D) (0,-1)
Show full solution
Correct answer: C) (-1,0)
(cos π,sin π)=(-1,0).
SAT trap: π radians points left.
COTERMINAL AND REFERENCE ANGLES
HARD
Question 27
What point on the unit circle corresponds to 3π/2?
Which choice is correct?
A) (0,1)
B) (1,0)
C) (-1,0)
D) (0,-1)
Show full solution
Correct answer: D) (0,-1)
(cos 3π/2,sin 3π/2)=(0,-1).
SAT trap: 3π/2 points downward.
COTERMINAL AND REFERENCE ANGLES
HARD
Question 28
Which radian measure is equivalent to 315°?
Which choice is correct?
A) 5π/4
B) 3π/2
C) 7π/4
D) 11π/6
Show full solution
Correct answer: C) 7π/4
315(π/180)=7π/4.
SAT trap: Reduce 315/180.
COTERMINAL AND REFERENCE ANGLES
HARD
Question 29
Which degree measure is equivalent to 11π/6?
Which choice is correct?
A) 300°
B) 315°
C) 330°
D) 345°
Show full solution
Correct answer: C) 330°
(11π/6)(180/π)=330°.
SAT trap: Multiply 11 by 30.
COTERMINAL AND REFERENCE ANGLES
HARD
Question 30
An angle of -π/3 is coterminal with which positive angle between 0 and 2π?
Which choice is correct?
A) 2π/3
B) 4π/3
C) 5π/3
D) 7π/3
Show full solution
Correct answer: C) 5π/3
Add 2π: -π/3+2π=5π/3.
SAT trap: Add one full rotation to negative angles.
How Are Arc Length and Sector Area Tested?
These questions use s=rθ and A=(1/2)r²θ with angles measured in radians.
ARC LENGTH AND SECTOR AREA
MEDIUM
Question 31
A circle has radius 6 and central angle π/3 radians. What is the arc length?
Which choice is correct?
A) π
B) 2π
C) 3π
D) 6π
Show full solution
Correct answer: B) 2π
Arc length s=rθ=6(π/3)=2π.
SAT trap: The formula s=rθ requires radians.
ARC LENGTH AND SECTOR AREA
MEDIUM
Question 32
A circle has radius 10 and central angle π/2. What is the arc length?
Which choice is correct?
A) 5π
B) 10π
C) 15π
D) 20π
Show full solution
Correct answer: A) 5π
s=10(π/2)=5π.
SAT trap: Multiply radius by the radian measure.
ARC LENGTH AND SECTOR AREA
MEDIUM
Question 33
A circle has radius 8 and central angle 3π/4. What is the arc length?
Which choice is correct?
A) 3π
B) 4π
C) 6π
D) 8π
Show full solution
Correct answer: C) 6π
s=8(3π/4)=6π.
SAT trap: Cancel before multiplying.
ARC LENGTH AND SECTOR AREA
MEDIUM
Question 34
A circle has arc length 12 and radius 4. What is the central angle in radians?
Which choice is correct?
A) 2
B) 3
C) 4
D) 8
Show full solution
Correct answer: B) 3
θ=s/r=12/4=3 radians.
SAT trap: Radians can be non-π numbers.
ARC LENGTH AND SECTOR AREA
MEDIUM
Question 35
A circle has arc length 5π and radius 10. What is the central angle?
Which choice is correct?
A) π/4
B) π/2
C) π
D) 2π
Show full solution
Correct answer: B) π/2
θ=s/r=(5π)/10=π/2.
SAT trap: Divide arc length by radius.
ARC LENGTH AND SECTOR AREA
MEDIUM
Question 36
A sector has radius 6 and angle π/2. What is its area?
Which choice is correct?
A) 6π
B) 9π
C) 18π
D) 36π
Show full solution
Correct answer: B) 9π
Sector area=(1/2)r²θ=(1/2)(36)(π/2)=9π.
SAT trap: Use radians in the sector formula.
ARC LENGTH AND SECTOR AREA
MEDIUM
Question 37
A sector has radius 4 and angle π/3. What is its area?
Which choice is correct?
A) 4π/3
B) 8π/3
C) 16π/3
D) 8π
Show full solution
Correct answer: B) 8π/3
Area=(1/2)(16)(π/3)=8π/3.
SAT trap: Square the radius.
ARC LENGTH AND SECTOR AREA
MEDIUM
Question 38
A sector has area 18π and radius 6. What is its angle in radians?
Which choice is correct?
A) π/2
B) π
C) 3π/2
D) 2π
Show full solution
Correct answer: B) π
18π=(1/2)(36)θ=18θ, so θ=π.
SAT trap: Solve directly from A=(1/2)r²θ.
ARC LENGTH AND SECTOR AREA
HARD
Question 39
A sector has area 25π/4 and angle π/2. What is the radius?
Which choice is correct?
A) 3
B) 5
C) 10
D) 25
Show full solution
Correct answer: B) 5
25π/4=(1/2)r²(π/2)=r²π/4, so r²=25 and r=5.
SAT trap: Take the positive square root.
ARC LENGTH AND SECTOR AREA
HARD
Question 40
A 60° central angle in a circle of radius 9 has what arc length?
Which choice is correct?
A) 2π
B) 3π
C) 6π
D) 9π
Show full solution
Correct answer: B) 3π
60°=π/3, so s=9(π/3)=3π.
SAT trap: Convert degrees to radians before using s=rθ.
ARC LENGTH AND SECTOR AREA
HARD
Question 41
A 120° central angle in a circle of radius 6 has what sector area?
Which choice is correct?
A) 6π
B) 12π
C) 18π
D) 36π
Show full solution
Correct answer: B) 12π
120°=2π/3. Area=(1/2)(36)(2π/3)=12π.
SAT trap: Convert the angle first.
ARC LENGTH AND SECTOR AREA
HARD
Question 42
An arc is one-fourth of a full circle. What is its radian measure?
Which choice is correct?
A) π/4
B) π/2
C) π
D) 3π/2
Show full solution
Correct answer: B) π/2
One-fourth of 2π is π/2.
SAT trap: A full rotation is 2π.
ARC LENGTH AND SECTOR AREA
HARD
Question 43
A sector is one-third of a circle. What is its central angle in radians?
Which choice is correct?
A) π/3
B) 2π/3
C) π
D) 4π/3
Show full solution
Correct answer: B) 2π/3
One-third of 2π is 2π/3.
SAT trap: Use a fraction of the full rotation.
ARC LENGTH AND SECTOR AREA
HARD
Question 44
A circle has circumference 20π. What is the arc length for an angle of 72°?
Which choice is correct?
A) 2π
B) 4π
C) 5π
D) 8π
Show full solution
Correct answer: B) 4π
72° is 1/5 of 360°, so the arc is (1/5)(20π)=4π.
SAT trap: A degree fraction of the circle also works.
ARC LENGTH AND SECTOR AREA
HARD
Question 45
A sector has area 40π and represents 40% of a circle. What is the circle’s total area?
Which choice is correct?
A) 80π
B) 100π
C) 120π
D) 160π
Show full solution
Correct answer: B) 100π
40π is 0.40 of the total, so total area=40π/0.40=100π.
SAT trap: Divide by the sector fraction.
Practice More SAT Geometry and Trigonometry
Build accuracy with arc length, sector area, and circular-motion models.
How Are Radians and Degrees Used in Applications?
These questions combine special-angle trigonometry, rotations, wheels, gears, and clocks.
TRIGONOMETRY AND ROTATION APPLICATIONS
HARD
Question 46
If θ=π/6, what is sin θ?
Which choice is correct?
A) 1/2
B) √2/2
C) √3/2
D) 1
Show full solution
Correct answer: A) 1/2
π/6=30°, and sin 30°=1/2.
SAT trap: Convert to a familiar special angle.
TRIGONOMETRY AND ROTATION APPLICATIONS
HARD
Question 47
If θ=π/3, what is cos θ?
Which choice is correct?
A) 1/2
B) √2/2
C) √3/2
D) 1
Show full solution
Correct answer: A) 1/2
π/3=60°, and cos 60°=1/2.
SAT trap: Do not confuse sine and cosine values.
TRIGONOMETRY AND ROTATION APPLICATIONS
HARD
Question 48
If θ=3π/4, what is sin θ?
Which choice is correct?
A) -√2/2
B) √2/2
C) -1/2
D) 1/2
Show full solution
Correct answer: B) √2/2
3π/4=135°, which has reference angle 45° in Quadrant II, where sine is positive.
SAT trap: Determine the quadrant sign.
TRIGONOMETRY AND ROTATION APPLICATIONS
HARD
Question 49
If θ=5π/6, what is cos θ?
Which choice is correct?
A) -√3/2
B) -1/2
C) 1/2
D) √3/2
Show full solution
Correct answer: A) -√3/2
5π/6=150°, reference angle 30°, and cosine is negative in Quadrant II.
SAT trap: Use the reference angle and quadrant.
TRIGONOMETRY AND ROTATION APPLICATIONS
HARD
Question 50
If θ=7π/4, what is tan θ?
Which choice is correct?
A) -1
B) -√3
C) 1
D) √3
Show full solution
Correct answer: A) -1
7π/4=315°, reference angle 45°, and tangent is negative in Quadrant IV.
SAT trap: Tangent is negative in Quadrants II and IV.
TRIGONOMETRY AND ROTATION APPLICATIONS
HARD
Question 51
A wheel rotates through 5π radians. How many full rotations is this?
Which choice is correct?
A) 1
B) 2
C) 2.5
D) 5
Show full solution
Correct answer: C) 2.5
Each full rotation is 2π, so 5π/(2π)=2.5.
SAT trap: Divide by 2π.
TRIGONOMETRY AND ROTATION APPLICATIONS
HARD
Question 52
A gear turns through 900°. How many full rotations is this?
Which choice is correct?
A) 1.5
B) 2
C) 2.5
D) 3
Show full solution
Correct answer: C) 2.5
900/360=2.5 rotations.
SAT trap: Divide degrees by 360.
TRIGONOMETRY AND ROTATION APPLICATIONS
HARD
Question 53
A Ferris wheel moves through 3π/2 radians. What fraction of one revolution is this?
Which choice is correct?
A) 1/4
B) 1/2
C) 3/4
D) 3/2
Show full solution
Correct answer: C) 3/4
(3π/2)/(2π)=3/4.
SAT trap: Compare with 2π.
TRIGONOMETRY AND ROTATION APPLICATIONS
HARD
Question 54
A clock’s minute hand moves 120° in how many minutes?
Which choice is correct?
A) 10
B) 15
C) 20
D) 30
Show full solution
Correct answer: C) 20
The minute hand moves 360° in 60 minutes, or 6° per minute. Thus 120/6=20.
SAT trap: Use a proportional rate.
TRIGONOMETRY AND ROTATION APPLICATIONS
HARD
Question 55
A clock’s hour hand moves π/3 radians in how many hours?
Which choice is correct?
A) 1
B) 2
C) 3
D) 4
Show full solution
Correct answer: B) 2
The hour hand moves 2π radians in 12 hours, or π/6 per hour. Thus (π/3)/(π/6)=2.
SAT trap: Use radians per hour.
What Do Hard Mixed Radians and Degrees Questions Look Like?
These questions combine conversions, arc models, sector models, approximations, and reference angles.
HARD MIXED RADIANS AND DEGREES
HARD
Question 56
An angle measures x° and 5π/6 radians. What is x?
Which choice is correct?
A) 120
B) 135
C) 150
D) 160
Show full solution
Correct answer: C) 150
(5π/6)(180/π)=150°.
SAT trap: Cancel π before multiplying.
HARD MIXED RADIANS AND DEGREES
HARD
Question 57
An angle measures 7π/9 radians. What is its degree measure?
Which choice is correct?
A) 120°
B) 130°
C) 140°
D) 150°
Show full solution
Correct answer: C) 140°
(7π/9)(180/π)=7×20=140°.
SAT trap: Simplify 180/9 first.
HARD MIXED RADIANS AND DEGREES
HARD
Question 58
An angle measures 315°. What is its radian measure?
Which choice is correct?
A) 5π/4
B) 3π/2
C) 7π/4
D) 11π/6
Show full solution
Correct answer: C) 7π/4
315(π/180)=7π/4.
SAT trap: Reduce 315/180.
HARD MIXED RADIANS AND DEGREES
HARD
Question 59
A circle has radius 12. An arc has length 8π. What is the central angle in degrees?
Which choice is correct?
A) 60°
B) 90°
C) 120°
D) 240°
Show full solution
Correct answer: C) 120°
θ=s/r=8π/12=2π/3, which is 120°.
SAT trap: Find radians first, then convert.
HARD MIXED RADIANS AND DEGREES
HARD
Question 60
A sector with radius 9 has area 27π. What is its angle in degrees?
Which choice is correct?
A) 60°
B) 90°
C) 120°
D) 180°
Show full solution
Correct answer: C) 120°
27π=(1/2)(81)θ, so θ=2π/3=120°.
SAT trap: Use the radian sector formula.
HARD MIXED RADIANS AND DEGREES
HARD
Question 61
An angle is 20% of a full rotation. What is it in radians?
Which choice is correct?
A) π/5
B) 2π/5
C) 3π/5
D) 4π/5
Show full solution
Correct answer: B) 2π/5
0.20(2π)=2π/5.
SAT trap: Use 2π for a full rotation.
HARD MIXED RADIANS AND DEGREES
HARD
Question 62
An angle is 2.4 radians. Which degree measure is closest?
Which choice is correct?
A) 118°
B) 128°
C) 138°
D) 148°
Show full solution
Correct answer: C) 138°
2.4(180/π)≈137.5°, closest to 138°.
SAT trap: Use 180/π for approximation.
HARD MIXED RADIANS AND DEGREES
HARD
Question 63
An angle is 225°. What is its reference angle in radians?
Which choice is correct?
A) π/6
B) π/4
C) π/3
D) 3π/4
Show full solution
Correct answer: B) π/4
225° has reference angle 45°=π/4.
SAT trap: Find the reference angle before converting.
HARD MIXED RADIANS AND DEGREES
HARD
Question 64
A point travels 15π units around a circle of radius 10. Through how many degrees does it move?
Which choice is correct?
A) 180°
B) 270°
C) 300°
D) 540°
Show full solution
Correct answer: B) 270°
θ=s/r=15π/10=3π/2=270°.
SAT trap: Arc length divided by radius gives radians.
HARD MIXED RADIANS AND DEGREES
HARD
Question 65
A sector has radius 8 and area 32π. What fraction of the circle is the sector?
Which choice is correct?
A) 1/4
B) 1/3
C) 1/2
D) 3/4
Show full solution
Correct answer: C) 1/2
The full circle area is 64π, so 32π/64π=1/2.
SAT trap: Compare sector area with full circle area.
What Do Student-Produced Response Questions Look Like?
Enter the requested conversion, arc length, rotation count, or reference angle.
STUDENT-PRODUCED RESPONSE
MEDIUM
Question 66
Convert 240° to radians. Enter the coefficient of π in simplest form as a fraction.
Enter your answer.
Show full solution
Correct answer: 4/3
240(π/180)=4π/3, so the coefficient is 4/3.
SAT trap: Enter only the requested numerical value.
STUDENT-PRODUCED RESPONSE
MEDIUM
Question 67
Convert 3π/5 radians to degrees.
Enter your answer.
Show full solution
Correct answer: 108
(3π/5)(180/π)=108°.
SAT trap: Enter only the requested numerical value.
STUDENT-PRODUCED RESPONSE
MEDIUM
Question 68
A circle has radius 5 and central angle 2 radians. What is the arc length?
Enter your answer.
Show full solution
Correct answer: 10
s=rθ=5(2)=10.
SAT trap: Enter only the requested numerical value.
STUDENT-PRODUCED RESPONSE
MEDIUM
Question 69
A wheel rotates through 8π radians. How many full rotations is this?
Enter your answer.
Show full solution
Correct answer: 4
8π/(2π)=4.
SAT trap: Enter only the requested numerical value.
STUDENT-PRODUCED RESPONSE
MEDIUM
Question 70
An angle of 150° has what reference angle in degrees?
Enter your answer.
Show full solution
Correct answer: 30
The reference angle is 180-150=30°.
SAT trap: Enter only the requested numerical value.
Common SAT Radians and Degrees Mistakes
| Mistake | Correction |
|---|---|
| Using the wrong conversion factor | Degrees to radians: multiply by π/180 |
| Forgetting that a full rotation is 2π | Use 360°=2π radians |
| Using degrees in s=rθ | Convert θ to radians first |
| Confusing the angle with its reference angle | Use the acute angle to the x-axis |
Two-Week SAT Radians and Degrees Study Plan
| Days | Focus |
|---|---|
| 1-3 | Q1-Q15: angle conversions |
| 4-7 | Q16-Q30: coterminal and reference angles |
| 8-10 | Q31-Q45: arc length and sector area |
| 11-14 | Q46-Q70 and error review |
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