Question

The height of a saw tooth in inches after time in seconds is represented by the function y = 0.4sin (15x + 1.5) - 0.2 for t > 0. Without graphing the function, determine the maximum height that the saw tooth reaches.

Answer 1

0.2 Inches

Explanation:

Given the height of the saw tooth represented by the function

`y = 0.4sin (15x + 1.5) - 0.2$ for $t > 0.`

Comparing with the general form of a trigonometric equation

`y = A sin(B(x + C)) + D`

Where:

• A =Amplitude
• Period =
  `2\pi/B`
• C=Phase Shift
• D=Vertical Shift

Amplitude, A=0.4

Vertical Shift (Midline),D = - 0.2

The maximum and minimum height of the sinusoidal function is given by:

[Min, Max]=[D-A, D+A]

=[-0.2-0.4, -0.2+0.4]

=[-0.6,0,2]

The maximum height that the sawtooth reaches is 0.2 inches.