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TAKE OUT YOUR “FITTING SINE CURVES TO DNA” WORKSHEET You should have a sketch with labeled maxes and mins. From these points, you can find the information we need to write an equation. Amplitude: ½(max—min) Vertical shift: Max—amp Period: find the differences in x-values of your maxes. Use this value to find ‘b’ (just enter it all in to your calculator and get a decimal. Horizontal shift: Trace up/down so that y= on the bottom is a close to your vertical shift value as you can get. Now move left/right until the cursor is over a point on your DNA strand. The x-value is the horizontal shift Reflection: Look at the point you used to find horizontal shift. If the strand goes up from here, it’s NOT reflected. Now you can write your equation!

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MODELING DATA WITH SINUSOIDAL FUNCTIONS Objectives: SWBAT Determine which types of data sets are best modeled by sinusoidal functions Write sinusoidal functions to model various situations Analyze sinusoidal functions to extrapolate information

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WHAT IS A SINUSOIDAL FUNCTION? Sine and cosine functions are often called sinusoids. Anything that behaves in a wave-like pattern that can be modeled by these functions is considered to be sinusoidal.

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Think of examples of things that either have a wave shape, or change/vary in a wave like pattern. WHAT ARE SOME THINGS THAT CAN BE MODELED BY SINUSOIDS? Sound waves Ocean Tides Temperature Ferris Wheels Daylight Hours Populations in a predator-prey environment Biorhythms Piston-crankshaft motions Swing/pendulum motion

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MUSIC, SINE WAVES, AND NOISE CANCELLING HEADPHONES Have you ever wondered how noise cancelling headphones work? It turns out the science behind this wonderful invention is actually just a whole lot of math! Let’s check it out! Bose has taken this idea and applied it to the seats in tractor-trailer trucks.

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FERRIS WHEELS A Ferris wheel with a radius of 25 feet is rotating at a rate of 3 revolutions per minute. When t = 0, a chair starts at the lowest point on the wheel, which is 5 feet above the ground. Write a model for the height h (in feet) of the chair as a function of the time t (in seconds).

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MODELING CLIMATE JanFebMarAprMayJunJulAugSepOctNovDec 28.631.137.146.456.065.871.670.263.152.643.933.9 The table below shows the 30-year monthly average temperature in Plymouth, MA. Plot the points on a graph Using the points, write a function for the graph. What kind of function should we write? Period:Vertical Shift: Amplitude:Horizontal Shift:

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MODELING CLIMATE Enter the data into L 1 and L 2 in the calculator Use a sine regression to generate a function to match the data. How does this compare to our function? JanFebMarAprMayJunJulAugSepOctNovDec 28.631.137.146.456.065.871.670.263.152.643.933.9

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EXAMPLE 1 Graph a vertical translation Graph y = 2 sin 4x + 3. SOLUTION STEP 1 Identify the amplitude, period, horizontal shift, and vertical shift. Amplitude:

EXAMPLE 1 Graph a vertical translation Graph y = 2 sin 4x + 3. SOLUTION STEP 1 Identify the amplitude, period, horizontal shift, and vertical shift. Amplitude:

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