4. Let x: (0, ) R be given by a(t) = (cost, cos t + log...

 

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4. Let x: (0, π)→ R² be given by a(t) = (cost, cos t + log tan m-½), where is the angle that the y axis makes with the vector a(t). The trace of a is called the tractrix (Fig. 1-9). Show that 2a B A SI a(t) Figure 1-8. The cissoid of Diocles. Figure 1-9. The tractrix. a. α is a differentiable parametrized curve, regular except at t = 7/2. b. The length of the segment of the tangent of the tractrix between the point of tangency and the y axis is constantly equal to 1. 4. Let x: (0, π)→ R² be given by a(t) = (cost, cos t + log tan m-½), where is the angle that the y axis makes with the vector a(t). The trace of a is called the tractrix (Fig. 1-9). Show that 2a B A SI a(t) Figure 1-8. The cissoid of Diocles. Figure 1-9. The tractrix. a. α is a differentiable parametrized curve, regular except at t = 7/2. b. The length of the segment of the tangent of the tractrix between the point of tangency and the y axis is constantly equal to 1.