How do you convert 90 degrees to radians?

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Answer


Yiwen

Multiply by a fraction which represents 1 revolution in both degrees and radians, you will find that 90∘=π2 radians

To convert from degrees to radians, consider a common measurement to determine a conversion fraction ratio.

1 revolution about a circle is both 360∘ and 2π radians, so if we wanted to represent this as an equation:

360 deg=2π rad⇒1=2π rad360 deg

The radian (SI image rad) is the SI unit for estimating points, and is the standard unit of rakish measure utilized in numerous regions of science. The length of a bend of a unit circle is numerically equivalent to the estimation in radians of the point that it subtends; one radian is just shy of 57.3 degrees (development at OEIS: A072097). The unit was once in the past a SI strengthening unit, however this classification was nullified in 1995 and the radian is presently viewed as a SI inferred unit.

Independently, the SI unit of strong edge estimation is the steradian. The radian is most ordinarily spoken to by the image rad. An elective image is c, the superscript letter c (for "roundabout measure"), the letter r, or a superscript R,[3] yet these images are rarely utilized as it tends to be effectively confused with a degree image (°) or a range (r). In this way, for instance, an estimation of 1.2 radians could be composed as 1.2 rad, 1.2 r, 1.2rad, 1.2c, or 1.2R.

Example1:

What is the formula to convert radians to degrees?

Before you begin the conversion process, you have to know that π radians = 180°, which is equivalent to going halfway around a circle. This is important because you'll be using 180/π as a conversion metric. This is because 1π radians is equal to 180/πdegrees. Multiply the radians by 180/π to convert to degrees.

Example2:

How long is a radian?

It follows that the magnitude in radians of one complete revolution (360 degrees) is the length of the entire circumference divided by the radius, or 2πr / r, or 2π. Thus 2πradians is equal to 360 degrees, meaning that one radian is equal to 180/π degrees. The relation can be derived using the formula for arc length.

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