A Direction Cosine Range

★ 6/10trigonometry Extrema analytic geometry

Problem

The point $P(x, y)$ satisfies

\begin{cases} x \leqslant 0,\\ y > x,\\ y < 2x + 1. \end{cases}

Find the range of possible values of $\dfrac{x + y}{\sqrt{x^2 + y^2}}$ .

Answer

Solution

Difficulty	6/10
Topics	trigonometry, Extrema, analytic geometry

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