First slide

Extreme values and Periodicity of Trigonometric functions

Question

$Min. value of \frac{1}{3 \sin θ - 4 \cos θ + 7}$

Easy

A

$\frac{5}{12}$
B

$\frac{1}{12}$
C

$\frac{7}{12}$
D

$\frac{1}{6}$

Solution

$R a n g e o f 3 \sin θ - 4 \cos θ + 7 i s [c - \sqrt{a^{2} + b^{2}}, c + \sqrt{a^{2} + b^{2}}] = [2, 12]$
$\sin c e 0 \notin [2, 12]$
$\Rightarrow$ $Min. value of the function is = \frac{1}{\max of (3 \sin θ - 4 \cos θ + 7)}$
$\begin{array}{l} = \frac{1}{7 + \sqrt{25}} \\ = \frac{1}{12} \end{array}$

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