Final answer:
To find the equation of the tangent line to the given curve at the point (π,−1), one must first determine the derivative of the function and evaluate it at x=π to find the slope. Then, use the point-slope form to obtain the equation of the tangent line.
Step-by-step explanation:
To find an equation of the tangent line to the curve y=(1+sinx)/cosx at the given point (π,−1), we need to determine the slope of the tangent line at that specific point. The slope (derivative of y with respect to x) represents the rate of change of the curve at the point where the tangent line touches the curve. The general process involves calculating the derivative of the function, then evaluating this derivative at the point of tangency to obtain the slope of the tangent line.
Here, the curve does not conform to the typical kinematic equations where a position is given by a time variable, as indicated in the provided information, which seems to refer to a different problem context. Instead, we calculate the derivative of the given function with respect to x and then substitute x=π to find the slope at the point (π, −1). Finally, we use the point-slope form of the equation of a line to write the equation of the tangent line.
In the context of the provided scenario, endpoints and positions are mentioned for determining the slope of a line representing motion over time. However, this information does not directly apply to our trigonometric function y=(1+sinx)/cosx and the computation of its tangent line at a specific point. The required calculation would involve trigonometric differentiation rather than calculating the slope from endpoints over a time interval.