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FInd the minimum and maximum value of 3\sin x+4\cos x

Option: 1

-\frac{7}{\sqrt{2}},\frac{7}{\sqrt{2}}


Option: 2

-4,4


Option: 3

-3,3


Option: 4

-5,5


Answers (1)

best_answer

\\\text {Range of function } \mathit{a}\sin x+\mathit{b}\cos x \text{ is given by }\\-\sqrt{\mathit{a^2+b^2}}\leq \mathit{a}\sin x+\mathit{b}\cos x\leq\sqrt{\mathit{a^2+b^2}}\\\\ \text{minimum value of }\mathit{3}\sin x+\mathit{4}\cos x \ is\ \-\sqrt{9+16}=-5 \ \\\text{maximum value of }\mathit{3}\sin x+\mathit{4}\cos x \ is\ \sqrt{9+16}=5 \

Posted by

Suraj Bhandari

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