Find the largest value in the expression 4-3sint. Find the largest value in the expression -4sint-1.

We will find the largest value of the function from the estimate of the range of values of the function.

1) y = 4 – 3 * sin t;

The sine function of an angle defines its value in the range from – 1 to 1. Let’s write the range of values in the form of a double inequality:

-1 <= sin t <= 1;

Multiply all parts of the inequality by -3:

-3 <= -3 * sin t <= 3;

Add 4 to all parts of the inequality:

1 <= 4 – 3 * sin t <= 7, which means that the largest value of the function is 7.

2) y = -4 * sin t – 1.

-1 <= sin t <= 1;

-4 <= -4 * sin t <= 4;

-5 <= -4 * sin t – 1 <= 3, so 3 is the largest value of the function.