Curve of Intersection of Two Surfaces in 3D: Plane and a Cylinder

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How to find the vector function which describes the curve of intersection of a plane and a cylinder, you'll need this when dealing with line integrals and stokes theorem.
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How can you arbitrarily define 1-t as sin(phi) and the square root fn as cos(phi)?

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can i know why you assume x=sin t, can I also assume x= cos t and the final answer for z would be z=1-cos t ?

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