**Convert between radians and degrees :**

**Degrees and radians are two measuring units of angles.**

If θ is a complete rotation (counter-clockwise) then θ = 2π radian. On the other hand we already know that one complete rotation (counter-clockwise) is 360°, consequently,

360° = 2π radians or 180° = π radian.

It follows that 1° = π /180 radian and 180°/ π = 1 radian.

- To Convert from degrees to radians, we have to multiply the given angle by π/180.
- To Convert from radians to degrees, we have to multiply the given radian by 180/π

The value of π in degrees is 180°

π = 180° 2π = 360° π/2 = 90° π/3 = 60° |
π/6 = 30° π/4 = 45° π/2 = 270° π/3 = 120° |

**Example 1 :**

Convert 150° into radians

**Solution :**

To convert degrees into radians, we have to multiply the given degree by π/180

150° = 150 x (π/180)

= 15π/18

= 5 π/6

Hence the conversion of 150° into radians is 5 π/6

**Example 2 :**

Convert 3 π/4 into degrees

**Solution :**

To convert radians into degrees, we have to multiply the given degree by 180/π

= (3 π/4) x (180/π)

= 540/4

= 135°

Hence the conversion of 3 π/4 into degrees is 135°.

**Example 3 :**

Convert 100° into radians

**Solution :**

To convert degrees into radians we have to multiply the given degree by π/180

= 100 x (π/180)

= 10π/18

= 5 π/9

Hence the conversion of 100° into radians is 5 π/9

**Example 4 :**

Convert π/8 into degrees

**Solution :**

To convert radians into degrees, we have to multiply the given degree by 180/π

= (π/8) x (180/π)

If we divide 180 by 8 we will get 22° as quotient and 4° as remainder. From here we have to convert this into minutes for that we have to multiply 4° by 60. So, we got 240 minutes. Then we have to divide this 240 by 8.

We have shown the above steps as the clear picture.

Hence the conversion of π/8 into degrees is 22° 30'.

**Example 5 :**

Convert 320° into radians

**Solution :**

To convert degrees into radians we have to multiply the given degree by π/180

= 320 x (π/180)

= 32π/18

= 16 π/9

Hence the conversion of 320° into radians is 16 π/9

**Example 6 :**

Convert 18π/5 into degrees

**Solution :**

To convert radians into degrees, we have to multiply the given degree by 180/π

= (18π/5) x (180/π)

= (18 x 180)/5

= 648°

Hence the conversion of 18π/5 into degree is 648°

After having gone through the stuff given above, we hope that the students would have understood "Convert between radians and degrees".

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