Classwork worksheet on converting angles between degrees, radians, and revolutions.

Let’s go step by step to verify and complete the table for converting between degrees, radians, and revolutions.

We are given the key conversion:
> 360° = 2π radians = 1 revolution

So we can use these relationships:

- To convert degrees → radians: multiply by π/180
- To convert radians → degrees: multiply by 180/π
- To convert degrees → revolutions: divide by 360
- To convert revolutions → degrees: multiply by 360
- To convert radians → revolutions: divide by 2π
- To convert revolutions → radians: multiply by 2π

Now let’s check each row in the table. The student has filled in some answers — we’ll verify them and fill any missing or incorrect ones.

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Row a: 180°

→ Radians: 180 × (π/180) = π ✔
→ Revolutions: 180 / 360 = 1/2 ✔
✔️ Correct

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Row b: 30°

→ Radians: 30 × (π/180) = π/6 ✔
→ Revolutions: 30 / 360 = 1/12 ✔
✔️ Correct

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Row c: ?° , π/2 rad, ? rev

Given: radians = π/2

→ Degrees: (π/2) × (180/π) = 90° ✔
→ Revolutions: (π/2) / (2π) = 1/4 ✔
✔️ Correct

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Row d: 135°, 3π/4 rad, ? rev

→ Check radians: 135 × (π/180) = (135/180)π = (3/4)π = 3π/4 ✔
→ Revolutions: 135 / 360 = simplify → divide numerator and denominator by 45 → 3/8 ✔
✔️ Correct

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Row e: 45°, ? rad, 1/8 rev

→ Radians: 45 × (π/180) = π/4 ✔
→ Check revolutions: 45 / 360 = 1/8 ✔
✔️ Correct

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Row f: 240°, ? rad, 2/3 rev

→ Radians: 240 × (π/180) = (240/180)π = (4/3)π = 4π/3 ✔
→ Revolutions: 240 / 360 = 2/3 ✔
✔️ Correct

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Row g: 225°, ? rad, ? rev

→ Radians: 225 × (π/180) = (225/180)π = (5/4)π = 5π/4 ✔
→ Revolutions: 225 / 360 = simplify → divide by 45 → 5/8 ✔
✔️ Correct

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Row h: 300°, 5π/3 rad, ? rev

→ Check radians: 300 × (π/180) = (300/180)π = (5/3)π = 5π/3 ✔
→ Revolutions: 300 / 360 = 5/6 ✔
✔️ Correct

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Row i: 264°, ? rad, 11/15 rev

→ First, check revolutions: 264 / 360 = ?

Simplify 264 ÷ 24 = 11, 360 ÷ 24 = 15 → so 11/15 ✔

→ Radians: 264 × (π/180) = (264/180)π

Simplify fraction: divide numerator and denominator by 12 → 22/15 → so 22π/15 ✔
✔️ Correct

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Row j: ?°, 1 rad, ? rev

Given: radians = 1

→ Degrees: 1 × (180/π) = 180/π ° ≈ but they wrote “180°/π” which is correct notation ✔
→ Revolutions: 1 / (2π) = 1/(2π) ✔
✔️ Correct

Note: They wrote “180°/π” — that’s acceptable as it means (180/π) degrees.

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Row k: 360π°, ? rad, π rev

Wait — this looks suspicious.

First, if angle is 360π degrees, that’s way more than one full circle.

But let’s compute:

→ Radians: 360π × (π/180) = (360π * π)/180 = 2π² radians → matches what’s written ✔

→ Revolutions: since 1 revolution = 360°, then number of revolutions = (360π) / 360 = π revolutions ✔

So even though 360π° is an unusual angle (it’s π full circles), mathematically it’s consistent.

BUT — look at the last column: they have “π” under Revolutions? That would mean π revolutions.

And indeed: 360π° ÷ 360° per revolution = π revolutions → correct.

However, note: in the radians column, they wrote “2π²” — which is correct because:

360π° × (π rad / 180°) = (360π × π)/180 = 2π² rad → yes.

So technically correct, although very large angles.

But wait — let’s double-check the original problem statement.

In row k, the degrees entry says “360π°”, radians says “2π²”, revolutions says “π”.

All conversions are mathematically correct.

However, there might be a typo in the problem — perhaps they meant 360°? But no, because then radians would be 2π, not 2π².

Alternatively, maybe they meant π radians? But no, the pattern suggests they’re testing understanding of scaling.

Actually, looking back — in row j, they had 1 radian → 180/π degrees → which is fine.

Similarly, here 360π degrees → 2π² radians → π revolutions → all consistent.

So ✔️ Correct.

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✔ All entries in the table are correctly filled!

There are no blanks left — every cell has been completed accurately based on the conversion formulas.

Final Answer: All values in the table are correct as shown. No corrections needed.