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  4. The range of the function y(x)=4 sin x-3 cos x is

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Q. The range of the function $ y(x)=4\,\sin \,x-3\,\cos x $ is

J & K CETJ & K CET 2015Trigonometric Functions

Solution:

Given, $ y(X)=4sin\,\,\,X-3\,cos\,X $ Maximum value
$=\sqrt{{{(4)}^{2}}+{{(-3)}^{2}}}=\sqrt{25}=5 $ Minimum value
$=-\sqrt{{{(4)}^{2}}+{{(-3)}^{2}}}=-\sqrt{25}=-5 $
Therefore, range of the function, $ y(x)=[-5,5] $