Chapter 6 Section 5 MA1032 Data, Functions & Graphs Sidney - - PowerPoint PPT Presentation

Chapter 6 Section 5

MA1032 Data, Functions & Graphs Sidney Butler

Michigan Technological University

November 6, 2006

S Butler (Michigan Tech) Chapter 6 Section 5 November 6, 2006 1 / 5

Modeling Problem

Suppose the tide rises 15 feet above and below mean sea-level. The tide patterns repeat every 12 hours. If the tide is at its lowest point at 10:00am, then find a formula giving the height of the tide relative to mean sea-level) as a function of the number of hours since 10:00am.

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Problem

Find the Amplitude, period, and horizontal shift for the following functions: y = −2 cos(πx − π

2 )

y = 23 sin(x/4 + 2)

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Exercise #32

Find a possible formula for the trigonometric function whose values are in the following table. x .1 .2 .3 .4 .5 .6 .7 .8 .9 1 g(x) 2 2.6 3 3 2.6 2 1.4 1 1 1.4 2

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Summary Graphing y = A sin(B(t − h)) + k and y = A cos(B(t − h)) + k Amplitude, period, frequency and horizontal shift Finding formulas for periodic functions using sine and cosine

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