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.
2. The sum of two angles is 1 radian and their difference is 1°. Find the angles in degrees.
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
Therefore, the required angles are (90/ π + ½)° and (90/π - 1/2)°.
● Measurement of Angles