The equation of the tangent to the curve x = t cost, y=t sin ⁡t at the origin, is 

The equation of the tangent to the curve x = t cost, y=t sin t at the origin, is 

  1. A

    x=0

  2. B

    y=0

  3. C

    x+y=0 

  4. D

    x-y=0

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    Solution:

    We have,

    x=tcost and y=tsint dxdi=costtsint and dydt=sint+tcost

    At the origin, we have 

    x=0,y=0tcost=0 and tsint=0t=0

    The slope of the tangent at t= 0 is

    dydx=dydtdxt=0=sint+tcostcosttsintt=0=0. 

    So, the equation of the tangent at the origin is

    y-0 = (x-0)  y=0.

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