Question type

Radians on the SAT

$π$ radians equals 180°. To convert radians to degrees, replace $π$ with 180: $\frac{7 π}{10} = \frac{7 \cdot 180}{10} = 126°$ . To convert degrees to radians, multiply by $\frac{π}{180}$ : $216° = \frac{216 π}{180} = \frac{6 π}{5}$ .

These questions convert an angle between degrees and radians, or mix the two, such as two angles of a triangle given in radians and the third asked for in degrees.

It appeared on two of the five official practice tests we analysed. A direct conversion is one step and Easy.

On 2 of 5 official practice tests
Desmos helps

Why students miss it

Multiplying by the wrong fraction. Degrees to radians is $\times \frac{π}{180}$ , not $\times \frac{180}{π}$ .

Answering in the wrong unit: the question may give radians and ask for degrees.

Forgetting that a triangle's angles sum to $π$ radians, the same as 180°.

How to spot it

An angle written with $π$ , such as $\frac{5 π}{12}$ .
"Radians" and "degrees" in the same question.

The method

Convert

$π$ radians $= 180°$ .

Radians to degrees: replace $π$ with 180.
Degrees to radians: multiply by $\frac{π}{180}$ and simplify.
Triangle angles in radians: they sum to $π$ .

With Desmos

Desmos converts in one line.

Type 7*180/10 for 7π/10 radians in degrees, or 216/180 for 216° as a multiple of π.

Two real questions

From the 1500prep bank, the way the app shows them. Answer first, then open the explanation.

1Question 1 of 2#700Geo

In triangle $A B C$ , the measure of angle $A$ is $\frac{π}{4}$ radians and the measure of angle $B$ is $\frac{5 π}{12}$ radians. What is the measure of angle $C$ , in degrees?

Pick an answer, then check it.

Show the answer and explanation

Convert using

π

radians

= 18 0^{\circ}

\frac{π}{4} = 4 5^{\circ}

and

\frac{5 π}{12} = 7 5^{\circ}

. Then

C = 180 - 45 - 75 = 60

2Question 2 of 2#687Geo

An angle has a measure of $21 6^{\circ}$ . What is the measure of this angle, in radians?

Pick an answer, then check it.

Show the answer and explanation

Multiply degrees by

\frac{π}{180}

216 \cdot \frac{π}{180} = \frac{216 π}{180} = \frac{6 π}{5}

. Note

21 6^{\circ}

exceeds

18 0^{\circ}

, so the answer must be more than

π

Questions students ask

How do you convert radians to degrees?

Replace π with 180 and simplify. 7π/10 radians is 7 × 180 ÷ 10 = 126°.

Are radians on the SAT?

Yes. They appeared on two of the five official digital SAT practice tests we analysed, usually as a conversion.

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