Intersection of parametric function with coordinate axes x ( t ) = t cos ⁡ t y ( t ) = t sin ⁡ t

Question

Intersection of parametric function with coordinate axes  x  (  t  )  =  t  cos  ⁡  t  y  (  t  )  =  t  sin  ⁡  t

treccinair · Accepted Answer

Step 1The equation  t  sin  ⁡  (  t  )  =  0gives us  t  =  0or  t  =  k  πwith  k  ∈      Z

Carly Cannon · Accepted Answer

Step 1Intersection with the x-axis means   y  =  0 :  x  =  t  cos  ⁡  t    0  =  t  sin  ⁡  tThe easiest solution is at   t  =  0 . If   t  ≠  0 you can use  0  =  sin  ⁡  (  t  )  ⇒  t  ∈  {  ±  π  ,  ±  2  π  ,  ±  3  π  }(because you can divide the second equation by t on both sides) to have  t  ∈  [  −  10  ,  10  ]Intersection with the y-axis means   x  =  0 :  0  =  t  cos  ⁡  t    y  =  t  sin  ⁡  tAgain   t  =  0 is a solution. For   t  ≠  0 we use  0  =  cos  ⁡  t  ⇒  t  ∈  {  ±  π      /    2  ,  ±  3  π      /    2  ,  ±  5  π      /    2  }

Intersection of parametric function with coordinate axes x ( t ) = t cos &

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