$\"\"$ \ \

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In a plane, if $\"\"$ is the angle between tangent line and $\"\"$ ( $\"\"$ -axis) then $\"\"$ . \ \

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where $\"\"$ is the arc length. \ \

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Chain rule of derivatives: $\"\"$ . \ \

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$\"\"$ \ \

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The angle of inclination is $\"\"$ . \ \

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$\"\"$ \ \

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Find $\"\"$ . \ \

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Arc length of the curve: $\"\"$ . \ \

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Formula for slope of the tangent $\"\"$ . \ \

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$\"\"$ \ \

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$\"\"$ \ \

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$\"\"$ \ \

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Find $\"\"$ . \ \

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$\"\"$ \ \

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Apply derivative on each side with respect to $\"\"$ . \ \

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$\"\"$ \ \

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$\"\"$ . \ \

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Substitute $\"\"$ . \ \

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$\"\"$ \ \

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Now $\"\"$ . \ \

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Substitute $\"\"$ and $\"\"$ . \ \

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$\"\"$ \ \

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$\"\"$

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$\"\"$ \ \

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Curvature formula: $\"\"$ . \ \

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$\"\"$ . \ \

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Therefore, if $\"\"$ is the angle between tangent line and $\"\"$ ( $\"\"$ -axis) in a plane then $\"\"$ . \ \

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$\"\"$ \ \

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$\"\"$ .