Question

maximum value of 3sinx + 3cosx​

Answer 1

$\underline{\underline{\text{ \LARGE{Basic idea}}}}$

For any function which is of the form,

$\sf f(x) = a\cos (x )+ b \sin (x)$

It's range is given by:

$\sf\left[ - \sqrt{ {a}^{2} + {b}^{2} } , \sqrt{ {a}^{2} + {b}^{2} } \right]$

We will use this concept to find maximum value of given function.

$\rule{100 mm}{1pt}$

$\underline{\underline{\text{ \LARGE{Solution}}}}$

Function we are provided with is,

$\sf f(x) = 3 \sin(x) + 3 \cos(x)$

Therefore it's range is:

$\implies [-\sqrt{3^2 + 3^2}, \sqrt{3^2+3^2}]$

$\implies [-\sqrt{9 + 9}, \sqrt{9 + 9}]$

$\implies [-\sqrt{18}, \sqrt{18}]$

$\implies [-3\sqrt{2}, 3\sqrt{2}]$

Hence the maximum value of our given function is 3√2.

$\rule{100mm}{1pt}$

$\underline{\underline{\text{ \LARGE{Learn More}}}}$

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