Convert Circular Measure

Convert circular measure systems to some other systems. The problems will be converted from circular system to sexagesimal system, circular system to centesimal system and also from circular system to circular system.

Worked-out problems to convert circular measure:

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

Solution:

π^c/8

= 180°/8, [Since, π^c = 180°]

= 22°30'

Again, π^c/8

= 200^g/8 [Since, π^c = 200^g)

= 25^g

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

2. The sum of two angles is 1 radian and their difference is 1°. Find the angles in degrees.

Solution:

Let x° and y° be the required angles and x > y. Then by problem,

x- y = 1 ………… (A)

Now, 180° = π radian

Therefore, x° = π x/180 radian and y° = πy/180 radian.

Therefore, π x/180 + πy/180 = 1

or, x + y = 180/π ………… (B)

Now, (A) + (B) gives, 2x = 180/π + 1

or, x= 90/π + 1/2

Again, (2) - (1) gives, 2y = 180/π - 1

or, y = 90/π - 1/2