Coefficients on an Arc

★ 7/10trigonometry Extrema Parametrization vectors

Problem

In a circular sector $AOB$ , $OA = OB = 1$ and $\angle AOB = \dfrac{\pi}{3}$ . A point $C$ on the arc $AB$ (excluding the endpoints) is written as

\overrightarrow{OC} = x\overrightarrow{OA} + y\overrightarrow{OB}.

1. Find the range of possible values of $x + y$ . 2. If $t = x + \lambda y$ attains a maximum value as $C$ varies, find the range of possible values of $\lambda$ .

Answer

Solution

Difficulty	7/10
Topics	trigonometry, Extrema, Parametrization, vectors

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