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Maximum value of trigonometric function

CMAT 2019 · Quantitative Techniques & Data Interpretation · Easy · Trigonometry

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The maximum value of 3cos⁡x+4sin⁡x+83\cos x + 4\sin x + 8 is:

  1. A.

    15

  2. B.

    3

  3. C.

    13

  4. D.

    7

Answer

C

Explanation

The maximum value of acos⁡x+bsin⁡x+ca\cos x + b\sin x + c is given by c+a2+b2c + \sqrt{a^2 + b^2}.

Max value =8+32+42=8+5=13= 8 + \sqrt{3^2 + 4^2} = 8 + 5 = 13.

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