Trigonometric Ratios Of Multiple And Sub Multiple Angles — MATHS STD 11 Science — Question
Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Ratios Of Multiple And Sub Multiple Angles1 Mark
Question
Write the maximum and minimum values of $3\cos\text{x}+4\sin\text{x}+5.$
✓
Answer
Let $\text{f(x)}=3\cos\text{x}+4\sin\text{x}+5$ We know that, $-\sqrt{3^2+4^2}\le3\cos\text{x}+4\sin\text{x}\le\sqrt{3^2+4^2}$ $\Rightarrow-\sqrt{9+16}\le3\cos\text{x}+4\sin\text{x}\le\sqrt{9+16}$ $\Rightarrow-\sqrt{25}\le3\cos\text{x}+4\sin\text{x}\le\sqrt{25}$ $\Rightarrow-5\le3\cos\text{x}+4\sin\text{x}\le5$ $\Rightarrow-5+5\le3\cos\text{x}+4\sin\text{x}+5\le5+5$ $\Rightarrow0\le3\cos\text{x}+4\sin\text{x}+5\le10$ Hence, minimum and maximum value of $3\cos\text{x}+4\sin\text{x}+5$ are 0 and 10 respectively.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.