Question

Match the following functions with it's correponding range.

• A. $[-5,5]$
• B. $[-1,1]$
• C. $[-6,6]$
• D. $[-2,2]$

Answer 1

For any real number $k,$ if $k\ge 0$
Then, $-k\le k\cos x\le k$
and if $k<0$
Then, $-k\ge k\cos x\ge k$

Thus using this method, we can find the corresponding ranges of the given trigonometric functions as:
$\cos x\in [-1,1]$
$-2\cos x\in [-2,2]$
$5\cos x\in [-5,5]$
$-6\cos x\in [-6,6]$