. Differential and integral calculus, an introductory course for colleges and engineering schools. 132 DIFFERENTIAL CALCULUS §96. 6. The Cardioid. This is the epicycloidin which b = a. Write down its equations,determine y, and find maximum andminimum abscissas and ordinates. Findthe slope of the tangent at the cusp,and at the points where the curve cutsOY. Calculate y. Draw the curve. 7. Discuss completely the hypocycloid 8. Discusswhen b = 2 a. completely the epicycloid 96. The Involute of the Circle. When in the epicycloid b = qo ,the rolling circle becomes a straight line, and may be regard
. Differential and integral calculus, an introductory course for colleges and engineering schools. 132 DIFFERENTIAL CALCULUS §96. 6. The Cardioid. This is the epicycloidin which b = a. Write down its equations,determine y, and find maximum andminimum abscissas and ordinates. Findthe slope of the tangent at the cusp,and at the points where the curve cutsOY. Calculate y. Draw the curve. 7. Discuss completely the hypocycloid 8. Discusswhen b = 2 a. completely the epicycloid 96. The Involute of the Circle. When in the epicycloid b = qo ,the rolling circle becomes a straight line, and may be regarded asthe taut portion of a string woundround the fixed circle and carryinga pencil, P, which traces the curveas the string is wound off the special epicycloid is termed theinvolute of the circle. We obtain itsparametric equations by determin-ing the limiting forms of equations(a), Art. 94, when b = oo. To thisend we write equations (a) in theform
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