PreCalc Need Help finding the lengths of circular arcs?
2. Find the lengths of both circular arcs of the unit circle connecting the point (-√2/2,-√2/2) and the endpoint of the radius the makes an angle of 8 radians with the positive horizontal axis
- jacob sLv 76 months ago
458.3662361° = 8 radians =
458.3662361° x π/180 = 10.17 π/4
Arc length of two points on the circle = θ x r where θ is angle between them in radius of the circle in our case r=1
so Angle of (-√2/2,-√2/2) with positive horizontal axis= tan^-1(-√2/2,/-√2/2)= 45°
The angle of other points is 8 radians= 458.3662361° with the positive horizontal axis so, the angle between them = 458.3662361° -(45°)= 413° or = 360° +(45 - 458)=-53 ° = - π/4 so arc length is - π/4 approx.