Question 13

The maximum value of 3 $$cosx+4 sinx+8$$ is

Solution

Let us consider the fucntion f(x) = $$a\cos x + b\sin x + c$$

The range of f(x) if given as $$c - \sqrt{a^2 + b^2} \leq f(x) \leq c + \sqrt{a^2 + b^2}$$

Then the maximum value of 3 $$cosx+4 sinx+8$$ is = 8 + $$\sqrt{3^2 + 4^2}$$

= 8 + 5 = 13

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