Conversion from
Circular to Sexagesimal System
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.
Solution:
πc/8We know, πc = 180°
πc/8 = 180°/8
πc/8 = 22.5° = 22° + 0.5°
[Now we will convert 0.5° to minute.
0.5° = (0.5 × 60)’ ; since 1° = 60’
= 30’]
πc/8 = 22° 30’
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.
Basic Trigonometry
Measurement of Trigonometric Angles
Relation between Sexagesimal and Circular
Conversion from Sexagesimal to Circular System
Conversion from Circular to Sexagesimal System
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