Let’s solve each problem step by step.
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Part A: Convert degrees to radians
To convert degrees to radians, use this rule:
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Multiply the degree measure by π/180
We’ll do each one carefully.
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1) 250°
250 × (π/180) = (250π)/180
Simplify: divide numerator and denominator by 10 → 25π/18
✔ Final:
25π/18
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2) –360°
–360 × (π/180) = –(360π)/180 = –2π
✔ Final:
–2π
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3) 64°
64 × (π/180) = (64π)/180
Simplify: divide numerator and denominator by 4 → 16π/45
✔ Final:
16π/45
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4) –9°
–9 × (π/180) = –(9π)/180 = –π/20
✔ Final:
–π/20
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5) 32°
32 × (π/180) = (32π)/180
Simplify: divide by 4 → 8π/45
✔ Final:
8π/45
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6) –171°
–171 × (π/180) = –(171π)/180
Simplify: divide by 9 → –19π/20
✔ Final:
–19π/20
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7) 900°
900 × (π/180) = (900π)/180 = 5π
✔ Final:
5π
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8) –783°
–783 × (π/180) = –(783π)/180
Let’s simplify:
Divide numerator and denominator by 9:
783 ÷ 9 = 87, 180 ÷ 9 = 20 → –87π/20
Can we simplify more? 87 and 20 have no common factors.
✔ Final:
–87π/20
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9) 45°
45 × (π/180) = (45π)/180 = π/4
✔ Final:
π/4
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Part B: Convert radians to degrees
To convert radians to degrees, use this rule:
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Multiply the radian measure by 180/π
The π will cancel out, leaving just a number in degrees.
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1) –11π/6
(–11π/6) × (180/π) = –11 × 180 / 6
First, 180 ÷ 6 = 30 → –11 × 30 = –330
✔ Final:
–330°
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2) π/2
(π/2) × (180/π) = 180/2 = 90
✔ Final:
90°
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3) –31π/18
(–31π/18) × (180/π) = –31 × 180 / 18
180 ÷ 18 = 10 → –31 × 10 = –310
✔ Final:
–310°
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4) π
π × (180/π) = 180
✔ Final:
180°
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5) –3π/10
(–3π/10) × (180/π) = –3 × 180 / 10
180 ÷ 10 = 18 → –3 × 18 = –54
✔ Final:
–54°
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6) 43π/60
(43π/60) × (180/π) = 43 × 180 / 60
180 ÷ 60 = 3 → 43 × 3 = 129
✔ Final:
129°
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7) 5π/12
(5π/12) × (180/π) = 5 × 180 / 12
180 ÷ 12 = 15 → 5 × 15 = 75
✔ Final:
75°
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8) 7π/3
(7π/3) × (180/π) = 7 × 180 / 3
180 ÷ 3 = 60 → 7 × 60 = 420
✔ Final:
420°
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9) –4π
–4π × (180/π) = –4 × 180 = –720
✔ Final:
–720°
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Final Answer:
Part A:
1) 25π/18
2) –2π
3) 16π/45
4) –π/20
5) 8π/45
6) –19π/20
7) 5π
8) –87π/20
9) π/4
Part B:
1) –330°
2) 90°
3) –310°
4) 180°
5) –54°
6) 129°
7) 75°
8) 420°
9) –720°
Parent Tip: Review the logic above to help your child master the concept of radian measure worksheet.
