Mathematics

Mathematics

Problem

Consider the curve r=eθr=e^{\theta}. Which of the following gives the equation of the tangent line at θ=a\theta=a in point–slope form? a) y−easin⁡a=cos⁡a−sin⁡asin⁡a+cos⁡a (x−eacos⁡a)y-e^{a}\sin a=\dfrac{\cos a-\sin a}{\sin a+\cos a}\,(x-e^{a}\cos a) b) y−easin⁡a=ea(sin⁡a+cos⁡a) (x−eacos⁡a)y-e^{a}\sin a=e^{a}(\sin a+\cos a)\,(x-e^{a}\cos a) c) y−easin⁡a=sin⁡a+cos⁡acos⁡a−sin⁡a (x−eacos⁡a)y-e^{a}\sin a=\dfrac{\sin a+\cos a}{\cos a-\sin a}\,(x-e^{a}\cos a) d) y−easin⁡a=sin⁡a−cos⁡acos⁡a+sin⁡a (x−eacos⁡a)y-e^{a}\sin a=\dfrac{\sin a-\cos a}{\cos a+\sin a}\,(x-e^{a}\cos a)

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