Since radius of this circle is 1, the length of an arc that subtends an angle of π/4 radians is π/4.
In Mathematics and Geometry, the arc length formed by a circle can be calculated by using the following equation (formula):
Arc length = πr × θ/180
Where:
- r represents the radius of a circle.
- θ represents the central angle in radians.
Since an angle of π/4 represent one-eighth of a whole turn, the length of an arc that subtends an angle of π/4 radians would be one-eighth of the whole circumference:
Arc length = 2π/8
Arc length = π/4 units.
In any unit circle, the length of an arc is exactly the measure of the central angle.