First slide

Extreme values and Periodicity of Trigonometric functions

Question

$The maximum value of 3 \cos x + 4 \sin x + 5 is$

Very Easy

A

1
B

5
C

10
D

7

Solution

$W e h a v e c - \sqrt{a^{2} + b^{2}} \leq a \cos θ + b \sin θ + c \leq c + \sqrt{a^{2} + b^{2}}$
$\begin{array}{l} ∴ Max. value = c + \sqrt{a^{2} + b^{2}} \\ = 5 + \sqrt{9 + 16} \\ = 10 \end{array}$

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