Pre-Calculus

Pre-Calculus Name
Chapter 6 – Graphs of Trigonometric Functions Period

6.6 Supplementary Worksheet

1. 
   Arnold is a bodybuilder whose weight fluctuates throughout the school year. His weight is given in the table below during the 10 months in which he cycles his training between bulking up, cutting weight, then getting back to his normal weight.
   

Sept	Oct	Nov	Dec	Jan	Feb	Mar	Apr	May	June	July
179	186	192	193	189	180	173	170	169	174	181

a) Find the amplitude of the sinusoidal function the can

model Arnold’s weight during his 10 month training cycle.
b) Find the vertical shift. c) What is the period?
d) Write a sine function to represent Arnold’s weight as a function of t , time in months, where September is t = 1.
e) According to your model, what is Arnold’s weight half way through his cycle in February? How does this value compare to his actual weight in February?
f) Use your calculator’s Sine Regression to find a sine function to represent Arnold’s weight.
2. The profit of a small business in town can be modeled by a cosine function. A high of $5000 was recorded on January 1^st, which reflected the sales generated during the holiday season. On July 1^st, a low of $2400 was recorded. Write a cosine function to represent the profit of the business as a function of the time of the year. Let t be the number of months from January 1^st , where January 1^st is t = 0.