IB Maths AA SL Topic 3 — Geometry & Trig Paper 1 & 2 🎯 Skill ~2 min practice

AA SL Degrees ↔ Radians skills

One simple identity links the two: 180° = π radians. From there, conversion is just a multiply. Memorise the common angles below and most exam questions take 3 seconds — no calculator needed.

The Method

180° = π radians the one identity that drives everything · ✓ in formula booklet

Direction 1

Degrees → Radians

multiply by π180

e.g. 60° × π180 = π3

Direction 2

Radians → Degrees

multiply by 180π

e.g. π4 × 180π = 45°

Common angles — memorise these

Degrees	Radians	Degrees	Radians
0°	0	180°	π
30°	π6	210°	7π6
45°	π4	225°	5π4
60°	π3	270°	3π2
90°	π2	360°	2π

If you know 30, 45, 60, 90° in radians, you can build the rest by multiplying.

Worked examples

WE 1 EASY

Convert 120° to radians, giving the answer in exact form.

step 1 — multiply by π/180 120 × (π / 180)step 2 — simplify the fraction = 120π / 180 = 2π / 3120° = 2π/3 radians “exact form” means leave π in — never decimals!

WE 2 MEDIUM

Convert 5π6 radians to degrees.

step 1 — multiply by 180/π (5π / 6) × (180 / π)step 2 — π cancels = 5 × 180 / 6 = 900 / 6 = 1505π/6 = 150° π always cancels when going from radians to degrees — clean answer every time!

WE 3 HARD

Convert 2.4 radians to degrees, giving the answer to 3 sf.

step 1 — multiply by 180/π 2.4 × (180 / π)step 2 — calculate = 2.4 × 57.2958… = 137.51 (full calculator)2.4 rad ≈ 138° (3 sf) when there’s no π in the radian, you’ll need a calculator. round at the end!

Practice questions

Try each one yourself first, then click the question to reveal the worked answer. Aim to do all 5 in under 3 minutes.

Q1 EASY Convert 90° to radians (exact form). Show answer ▼Hide answer ▲

90 × π/180 = 90π/180 π/2 radians

Q2 EASY Convert π3 radians to degrees. Show answer ▼Hide answer ▲

(π/3) × (180/π) = 180/3 60°

Q3 MEDIUM Convert 75° to radians (exact form). Show answer ▼Hide answer ▲

75 × π/180 = 75π/180 simplify (÷ 15) 5π/12 radians

Q4 MEDIUM Convert 7π4 radians to degrees. Show answer ▼Hide answer ▲

(7π/4) × (180/π) = 7 × 180/4 = 1260/4 315°

Q5 HARD Convert 1.8 radians to degrees, to 3 sf. Show answer ▼Hide answer ▲

1.8 × (180/π) = 1.8 × 57.2958… = 103.13… 1.8 rad ≈ 103° (3 sf) no π in the radian → use calculator value 180/π ≈ 57.296

⚠ Common mistakes

Multiplying by the wrong fraction. Going to radians, multiply by π180. Going to degrees, multiply by 180π. Mixing them up flips your answer wildly.
Forgetting “exact form” means leave π in. If asked for an exact answer, leave it as 2π3 — never convert to a decimal.
Calculator in degree mode when working in radians. Calculations like sin(π6) need radian mode — set it before you start.
Treating “radians” as a unit you can drop. Radians is dimensionless, but the question’s required form (degrees vs radians) is what matters — give the right one.
Cancelling π too early. When converting radians to degrees, the π in the radian and the π in the multiplier cancel — but only when both are present. If the radian is just a decimal (no π), you can’t cancel.
Not simplifying the fraction. 60° = 60π180, but the simplified form π3 is what examiners want.

📖

Want the theory?

Read the full Radian Measure notes for why radians are the “natural” unit, the link to the unit circle, and how arc length s = rθ only works when θ is in radians.

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