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Trigonometry › Trigonometric functions: period and extremes › Maximum and minimum

Maximum of a trigonometric quadratic in cosine

High school · ●●○○○ 20 pts

Find the maximum value of the function f(x)=sin⁡2x+3cos⁡x−34f(x)=\sin^{2}x+\sqrt{3}\cos x-\frac{3}{4} for x∈[0,π2]x\in\left[0,\frac{\pi}{2}\right].

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trigonometric identitiesoptimization