First slide

Extreme values and Periodicity of Trigonometric functions

Question

If $A = 13 \cos x + 3 \sqrt{3} \sin x + 4$ then

Moderate

A

$10 \leq A \leq 18$
B

$8 \leq A \leq 2$
C

$- 10 \leq A \leq 18$
D

$- 8 \leq A \leq 2$

Solution

Maximum value
$= 4 - \sqrt{169 + 27} = - 14 + 4 = - 10$
Minimum value
$= 4 + \sqrt{169 + 27} = 4 + 14 = 18 ∴ - 10 \leq A \leq 18$

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