Trigonometric Properties and Graphs

The great news is that we've already seen most of this.

• Let's start with trig properties:

• Now because these functions are so important for modeling physical phenomena, we give special names to some of the standard transformations to the sine (and cosine) functions.

  The function

  

  represents three transformations:

  1. a horizontal shift (right) by b units (the phase shift);
  2. a horizontal stretch by k (and note that as k gets bigger, the waves get shorter - of period ); and
  3. a vertical stretch by a factor of |a| (the amplitude).
  

  Examples: #45 and 48, p. 396.

• Let's revisit the
  

  (from Introduction to Global Climate Change, Arnold J. Bloom).

  What should the amplitude of the wiggles be? What is the period?

  

• Here's your homework: let's get started on it.

  Pp. 396--, #3, 5, 6, 9, 14, 17, 19, 23, 28, 29, 31, 32, 33, 36, 38, 43, 44, 47, 49, and 50;

  Pp. 405--, #9, 10, 11, 12, 19, 20, 27, 28, 29, 36, 49, and 53.