Honors Pre-Calculus Notes: _____________________________________________ Unit 4 Day 2 Notes Basic Form: __________________________________________________________________________________________________________________ Amplitude: __________________________________________________________________________________________________________________

Period: _______________________________________________________________________________________________________________________

Phase Shift: __________________________________________________________________________________________________________________

Determine the amplitude and period of each function.

Give the amplitude and period of each function. Then sketch the graph of the function over -2π < x < 2π using the key points for each function.

8. Write the cosine function as a phase shift of the sine function. 9. Write the sine function as a phase shift of the cosine function. Sinusoidal Modeling

1.

2. Throughout the day, the depth of water at the end of a dock in Bar Harbor, Maine varies with the tides. The table shows the depths (in feet) at various times during the morning. (Source: Nautical Software, Inc.) a. Use a trigonometric function to model the data. b. Find the depths at 9 A.M. and 3 P.M. c. A boat needs at least 10 feet of water to moor at the dock. During what times in the afternoon can it safely dock?