Question

Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. The curve is defined by the equations x = t cos(t) and y = t sin(t). Find the equation of the tangent when t = ?

Answer 1

To find the equation of the tangent to the curve at a given point, we need to find the derivative of the curve at that point and use the point-slope form to write the equation of the tangent line.

Step-by-step explanation:

To find the equation of the tangent to the curve at the point corresponding to the given value of the parameter, we need to find the derivative of the curve at that point. Let's find the derivative:

x = t*cos(t) => dx/dt = cos(t) - t*sin(t)

y = t*sin(t) => dy/dt = sin(t) + t*cos(t)

Now, substitute t = ?? into dx/dt and dy/dt to get the slopes of the tangent. Finally, use the point (x, y) at t = ?? and the slope of the tangent to find the equation of the tangent line using the point-slope form.