A Parameterized Completion

★ 7/10trigonometryExtremaalgebraCompleting the Square

Problem

Find the range of the function

f(x)=sin⁡xcos⁡x+sin⁡x+25cos⁡x,x∈R.f(x) = \sin x\cos x + \sin x + \frac{2}{5}\cos x, \qquad x \in \mathbb{R}.

Answer

Solution

Difficulty7/10
Topicstrigonometry, Extrema, algebra, Completing the Square

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