Find the largest and smallest value of the expression -5 | sinx |.

We have a function:

y = -5 * | sin x |.

To determine the largest and smallest values, we immediately note that the trigonometric sine function, regardless of the value of its argument, takes values in the interval [-1; one]. And the modulus of any value takes strictly non-negative values. Let’s write the range of values in the form of a double inequality:

-1 <= sin x <= 1;

0 <= | sin x | <= 1;

Multiply all parts of the double inequality by minus five:

-5 <= -5 * | sin x | <= 0.

-5 and 0 are the smallest and largest values of the function.