For the parametric curves x = sin t, y = cos t, dy/dx simplifies to which expression?

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Multiple Choice

For the parametric curves x = sin t, y = cos t, dy/dx simplifies to which expression?

Explanation:
In parametric form, the slope dy/dx is found by dividing the rate of change of y with respect to t by the rate of change of x with respect to t. Here, dx/dt = cos t and dy/dt = -sin t, so dy/dx = (dy/dt)/(dx/dt) = (-sin t)/(cos t) = -tan t, for all t where cos t ≠ 0. Therefore the slope simplifies to -tan t. At t where cos t = 0, the slope is undefined, corresponding to vertical tangents on the curve.

In parametric form, the slope dy/dx is found by dividing the rate of change of y with respect to t by the rate of change of x with respect to t. Here, dx/dt = cos t and dy/dt = -sin t, so dy/dx = (dy/dt)/(dx/dt) = (-sin t)/(cos t) = -tan t, for all t where cos t ≠ 0. Therefore the slope simplifies to -tan t. At t where cos t = 0, the slope is undefined, corresponding to vertical tangents on the curve.

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