Question

Convert 2π/3
in terms of sexagesimal system (degrees)
1) 400
2) 500
3) 60°
4) 1200​

Answer 1

Answer:

500

Step-by-step explanation:

Answer 2

Answer:

Systems are the three different systems of measuring angles. Sexagesimal system is also known as English system and centesimal system is known as French system.

To convert the one system to the other system its very necessary to know the relation among the Sexagesimal system, Centesimal system and Circular system.

The relation between Sexagesimal, Centesimal and Circular systems are discussed below:

Since 90° = 1 right angle, hence, 180° = 2 right angles.

Again, 100g = 1 right angle; hence, 200g = 2 right angles.

And, πc = 2 right angles.

Therefore, 180° = 200g = πc.

Step-by-step explanation:

Let, D°, Gg and Rc be the sexagesimal, centesimal and circular measures respectively of a given angle.

Now, 90° = 1 right angle

Therefore, 1° = 1/90 right angle

Therefore, D° = D/90 right angle

Again, 100g = 1 right angle

Therefore, 1g = 1/100 right angle

Therefore, Gg = G/100 right angle.

And, 1c = 2/π right angle

Therefore, Rc = 2R/π right angle.

Therefore we have,

D/90 = G/100 = 2R/π

or,

D/180 = G/200 = R/π

1. The circular measure of an angle is π/8; find its value in sexagesimal and centesimal systems.

Solution:

πc/8

= 180°/8, [Since, πc = 180°)

= 22°30'

Again, πc/8

= 200g/8 [Since, πc = 200g)

= 25g

Therefore, the sexagesimal and centesimal measures of the angle πc/8 are 22°30' and 25g respectively.

hope this will help you