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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

  1. 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

  2. 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. S Butler (Michigan Tech) Chapter 6 Section 5 November 6, 2006 2 / 5

  3. Problem Find the Amplitude, period, and horizontal shift for the following functions: y = − 2 cos( π x − π 2 ) y = 23 sin( x / 4 + 2) S Butler (Michigan Tech) Chapter 6 Section 5 November 6, 2006 3 / 5

  4. Exercise #32 Find a possible formula for the trigonometric function whose values are in the following table. 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1 x g ( x ) 2 2.6 3 3 2.6 2 1.4 1 1 1.4 2 S Butler (Michigan Tech) Chapter 6 Section 5 November 6, 2006 4 / 5

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

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