Convert 3 radians to degrees

Step by step

The question

Question: change 3 radians to degrees.

1 Write the rule

Radians are another way to measure an angle.

A half turn is 180°.

In radians, a half turn is π.

So π = 180°.

We divide both sides by π.

One radian is 180° over π.

Careful!

To get degrees, π must cancel.

So π goes at the bottom.

2 Multiply

3 radians is 3 times one radian.

So we multiply by 180° over π.

Top times top: 540°.

3 Work it out

There is no π to cancel.

So we use the calculator: π is about 3.1416.

540 divided by π is about 171.887.

To the nearest tenth, 3 radians ≈ 171.9°.

4 Check

Let's check: go back to radians.

Times π over 180.

We get about 3: back to 3, close because we rounded.

So it is right!

Let's look back.

First: write the rule.

Then: multiply.

Then: work it out.

Last: check.