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# Why is pi radians equal to 180 degrees?

## Why is pi radians equal to 180 degrees?

We’re talking about radian measure of angles. 180 degrees equals pi radians, so to get one degree divide both sides by 180. One degree is pi over 180 and if you want a decimal value for this you can use your calculator pi divided by 180, this is approximately . 0175.

### What is pi 4 radians in degrees?

Table of angles

15° Pi / 12 16.67
30° Pi / 6 33.33
36° Pi / 5 40.00
45° Pi / 4 50.00

#### What is Pi in degrees?

What does PI equal in radians?

180π degrees
So one radian is equal to 180π degrees, which is approximately 57.3∘. Since many angles in degrees can be expressed as simple fractions of 180, we use π as a basic unit in radians and often express angles as fractions of π.

Is pi 360 degrees?

A circle has 360 degrees or 2pi radians — going all the way around is 2 * pi * r / r. So a radian is about 360 /(2 * pi) or 57.3 degrees.

## Why is a full circle 2 pi?

Originally Answered: Why are there 2\pi radians in a circle? Because the length of the circumference of a circle is exactly 2*pi times the radius and by definition 1 radian is the angle subtended by a portion of the circumference equal in length to the radius. To 1 radia “goes into” the total circumference 2*pi times.

### What is 3 PI 4 radians converted to degrees?

135 degrees
The degree form when we convert $\dfrac{{3\pi }}{4}$ radians to degrees is equal to 135 degrees.

#### What is the exact value of cos PI 4?

√2/2
The actual value of cos pi/4 is √2/2 in radical form and 0.7071 in decimal form.

Is pi 3.14 or 180?

π radians is approximately 3.14 radians. So, just approximating the constant π as 3.14 gives you the same kind of thing; a number of radians, as an angle measure. On the other hand, it’s completely accurate to say that π radians =180∘.

How many radians is 90 degrees in terms of pi?