Question

The height of a saw tooth in inches after time in seconds is represented by the function y = 0.3sin (30x + 1.5) - 0.1 for t > 0. Without graphing the function, determine the range that the saw tooth covers.

Answer 1

-1 ≤ sin (30x + 1.5) ≤ 1

Multiply all the terms by 0.3

-1*0.3 ≤ 0.3 sin (30x + 1.5) ≤ 1*0.3

Substract 1 from all the terms

-1*0.3 - 1 ≤ 0.3 sin (30x + 1.5) - 1 ≤ 1*0.3 -1

-1.3 ≤ 0.3 sin (30x + 1.5) - 1 ≤ 0.7

-1.3 ≤ height ≤ 0.7

The range of the height of the saw tooth is from -1.3 inches to 0.7 inches