A curve has parametric equations x = tan^2(t)

A curve has parametric equations x = tan^2(t) y = sint,  0 < t < π/2 (a) Find an expression for dy/dx in terms of t. You need not simplify your answer. 

To find the expression for dy/dx, we can differentiate both x and y with respect to t using the chain rule.

Given:

x = tan^2(t)

y = sint

Differentiating x with respect to t:

dx/dt = d/dt (tan^2(t))

Using the chain rule:

dx/dt = 2tan(t) * sec^2(t)

Differentiating y with respect to t:

dy/dt = d/dt (sint)

dy/dt = cost

Now, to find dy/dx, we can divide dy/dt by dx/dt:

dy/dx = (dy/dt) / (dx/dt)

dy/dx = (cost) / (2tan(t) * sec^2(t))

Therefore, the expression for dy/dx in terms of t is:

dy/dx = (cost) / (2tan(t) * sec^2(t))

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