If maximum vertical distance between the graphs of $y = 2 + 3 sin x$ and $y = 4 cos x - 3$ is $k,$ then the characteristic of ${log}_{10}$ $k$ is :

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Solution

The correct option is C $1$
Given curves are,
$y_{1} = 2 + 3 s i n x, y_{2} = 4 c o s x - 3$

The vertical distance between two curves is given by,
$y_{1} - y_{2} = 2 + 3 s i n x - 4 c o s x + 3 = 3 s i n x - 4 c o s x + 5$

Then $(y_{1} - y_{2})_{m a x} = (\sqrt{3^{2} + (- 4)^{2}} + 5) = \sqrt{25} + 5$

$= 10$
Hence K=10

The characterstics of $l o g_{10} k = l o g_{10} 10 = 1$

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