Anonymous
Anonymous asked in Science & MathematicsMathematics · 6 months ago

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

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  • 6 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. 

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