Worked-out problems on the conversion from circular to sexagesimal system:
1. In a right-angled triangle the difference between two acute angles is 2π/5. Express these two angles in terms of radian and degree.
Solution:Let the acute angles be xc and yc. (According to the condition of the problem:
x + y = π/2 and x - y = 2π/5
Solving these two equations we get;
x = 1/2 (π/2 + 2π/5)
x = 1/2 (5π + 4π/10)
x = 1/2 (9π/10)
x = 9π/20
and y = 1/2 (π/2 - 2π/5)
y = 1/2 (5π - 4π/10)
y = 1/2 (π/10)
y = π/20
Again, x = (9 × 180°)/20 = 81°
y = 180°/20 = 9°
2. The circular measure of an angle is π/8; find its value in sexagesimal systems.
Therefore, the sexagesimal measures of the angle π/8 is 22° 30’
The above solved problems help us to learn in trigonometry, about the conversion from circular to sexagesimal system.