Final answer:
To find the slope of the tangent line to the polar curve r = 7 + 4Cos(θ) at θ = π/3, calculate the derivative of the radial function with respect to θ, evaluate it at the given angle, and use the slope formula for polar coordinates.
Step-by-step explanation:
Finding the Slope of a Polar Curve
To find the slope of the tangent line to the curve r = 7 + 4Cos(θ) at the point specified by θ = π/3, we need to use calculus as straightforward slope calculations like in Cartesian coordinates don't directly apply. The slope in polar coordinates at a given angle is determined by the derivative of the radial function with respect to θ and the derivative of the radial function with respect to radius. These derivatives are used to compute the slope of the tangent as discussed below:
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Note that this process involves calculus, specifically differentiation. If you are not familiar with differentiation and calculus, you might need to review these mathematical topics to fully understand the process to derive the slope of a tangent line in polar coordinates.