Question

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

• A. $(-5,5)$
• B. $(-5,5]$
• C. $[-5,5)$
• D. $[-5,5]$

Answer 1

Answer: (D)

Given, $y(X)=4sinX-3cosX$ 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, $y(x)=[-5,5]$