Question

The Range of $f\left(x\right)=3\sin x+4\cos x+5$ is

Answer 1

The range of trigonometric equations of type $a\sin x+b\cos x+c$ id given as $[c-\sqrt{a^2+b^2},c+\sqrt{a^2+b^2}]$

Here $a=3,b=4,c=5$

So the range is $[5-\sqrt{3^2+4^2},5+\sqrt{3^2+4^2}]$

$[5-5,5+5]=[0,10]$

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