(D) The expression is of the form $a\sin \theta + b\cos \theta$,where $a = 3$ and $b = 4$.The range of the function $f(\theta) = a\sin \theta + b\cos

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(D) The expression is of the form $a\sin \theta + b\cos \theta$,where $a = 3$ and $b = 4$.The range of the function $f(\theta) = a\sin \theta + b\cos \theta$ is $[-\sqrt{a^2 + b^2}, \sqrt{a^2 + b^2}]$.Substituting the values,we get the range as $[-\sqrt{3^2 + 4^2}, \sqrt{3^2 + 4^2}] = [-\sqrt{9 + 16}, \sqrt{9 + 16}] = [-5, 5]$.Therefore,the minimum value is $-5$.

Class 11 Mathematics Trigonometric Functions Maximum and minimum values of trigonometrical functions, Conditional trigonometrical identities

Easy

The minimum value of $3\sin \theta + 4\cos \theta $ is

A
$5$
B
$1$
C
$3$
D
$-5$

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Trigonometric Functions

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Maximum and minimum values of trigonometrical functions, Conditional trigonometrical identities

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The minimum value of $3\sin \theta + 4\cos \theta $ is

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