Convert 3π/4 to degrees

Step by step

The question

Question: change 3π/4 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

3π/4 radians is 3π/4 times one radian.

So we multiply by 180° over π.

π on top and π at the bottom: π over π is 1.

Cross them out.

What is left: 3 × 180° over 4.

3 Make it simpler

First 180 divided by 4: 45.

Dividing first keeps the numbers small.

So it is 3 times 45°.

So 3π/4 = 135°.

4 Check

Let's check: go back to radians.

Times π over 180.

We get 3π/4 again.

So it is right!

Let's look back.

First: write the rule.

Then: multiply.

Then: make it simpler.

Last: check.