Expert: Sherry Wallin - 5/9/2009

Question
I have to wirte an essay for pre-cal and i need some help.  How are trigonometric graphs used in the workplace?

Answer
Hi Francesca~
    The two most common trigonometric graphs that are used are the sine function and the cosine function and of the two the sine function is most common although the cosine function is just the sine function shifted 90 degrees. With that said let's talk about the sine function.
One application in our lives is of AC/DC electricity. The behavior of AC/DC electricity can be modeled by the sine graph. Trigonometric functions are periodic which means they are cyclical which means they repeat a pattern, so really anything that is cyclical or repeats a pattern can be represented by the sine graph. The other common place sine graphs are used is to model waves whether it be sound waves, microwaves, heat waves, vibrations they all follow the pattern of the sine function. The height of the wave will be the coefficient in front of the function. For example Asinx the A is the amplitude which is how high the wave is. I can further represent the form of the equation and put a B in in front of the x as in AsinBx and now the B represents the amount of time it takes for the function or pattern to repeat itself otherwise known as the period. When B is bigger than one the function repeats itself quite rapidly and when it is between 0 and 1 then it repeats much slower.

Math Prof