CONVERSION BETWEEN DEGREES AND RADIANS

Example 1-8 : Convert degrees to radians :

Example 1 :

45°

Solution :

To convert the given angle measure 45° to radians, multiply 45° by π/180°.

= 45° x (π/180°)

= 45°π/180°

= π/4 radians

Example 2 :

90°

Solution :

To convert the given angle measure 90° to radians, multiply 90° by π/180°.

= 90° x (π/180°)

= 90°π/180°

= π/2 radians

Example 3 :

135°

Solution :

To convert the given angle measure 135° to radians, multiply 135° by π/180°.

= 135° x (π/180°)

= 135°π/180°

= 3π/4 radians

Example 4 :

180°

Solution :

To convert the given angle measure 180° to radians, multiply 180° by π/180°.

= 180° x (π/180°)

= 180°π/180°

= π radians

Example 5 :

225°

Solution :

To convert the given angle measure 225° to radians, multiply 225° by π/180°.

= 225° x (π/180°)

= 225°π/180°

= 5π/4 radians

Example 6 :

270°

Solution :

To convert the given angle measure 270° to radians, multiply 270° by π/180°.

= 270° x (π/180°)

= 270°π/180°

= 3π/2 radians

Example 7 :

315°

Solution :

To convert the given angle measure 315° to radians, multiply 315° by π/180°.

= 315° x (π/180°)

= 315°π/180°

= 7π/4 radians

Example 8 :

360°

Solution :

To convert the given angle measure 360° to radians, multiply 360° by π/180°.

= 360° x (π/180°)

= 360°π/180°

= 2π radians

Example 9 :

22.5°

Solution :

To convert the given angle measure 22.5° to radians, multiply 22.5° by π/180°.

= 22.5° x (π/180°)

= 22.5°π/180°

= π/8 radians

Example 10 :

67.5°

Solution :

To convert the given angle measure 67.5° to radians, multiply 67.5° by π/180°.

= 67.5° x (π/180°)

= 67.5°π/180°

= 3π/8 radians

Example 11-20 : Convert radians to degrees :

Example 11 :

π/5

Solution :

To convert the given angle measure π/5 to degrees, multiply π/5 by 180°/π.

= (π/5) x (180°/π)

= 180°π/5π

= 180°/5

= 36°

Example 12 :

π/20

Solution :

To convert the given angle measure π/20 to degrees, multiply π/20 by 180°/π.

= (π/20) x (180°/π)

= 180°π/20π

= 180°/20

= 9°

Example 13 :

π/18

Solution :

To convert the given angle measure π/18 to degrees, multiply π/18 by 180°/π.

= (π/18) x (180°/π)

= 180°π/18π

= 180°/18

= 10°

Example 14 :

π/10

Solution :

To convert the given angle measure π/10 to degrees, multiply π/10 by 180°/π.

= (π/10) x (180°/π)

= 180°π/10π

= 180°/10

= 18°

Example 15 :

π/9

Solution :

To convert the given angle measure π/9 to degrees, multiply π/9 by 180°/π.

= (π/9) x (180°/π)

= 180°π/9π

= 180°/9

= 20°

Example 16 :

π/8

Solution :

To convert the given angle measure π/8 to degrees, multiply π/8 by 180°/π.

= (π/8) x (180°/π)

= 180°π/8π

= 180°/8

= 22.5°

Example 17 :

2π/5

Solution :

To convert the given angle measure 2π/5 to degrees, multiply 2π/5 by 180°/π.

= (2π/5) x (180°/π)

= (2π x 180°)/5π

= (2 x 180°)/5

= 360°/5

= 72°

Example 18 :

7π/20

Solution :

To convert the given angle measure 7π/20 to degrees, multiply 7π/20 by 180°/π.

= (7π/20) x (180°/π)

= (7π x 180°)/20π

= (7 x 180°)/20

= 1260°/20

= 63°

Example 19 :

5π/18

Solution :

To convert the given angle measure 5π/18 to degrees, multiply 5π/18 by 180°/π.

= (5π/18) x (180°/π)

= (5π x 180°)/18π

= (5 x 180°)/18

= 900°/18

= 50°

Example 20 :

7π/3

Solution :

To convert the given angle measure 7π/3 to degrees, multiply 7π/3 by 180°/π.

= (7π/3) x (180°/π)

= (7π x 180°)/3π

= (7 x 180°)/3

= 1260°/3

= 420°

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