DO NOW

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!

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

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.

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

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.

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).

MODELING CLIMATE JanFebMarAprMayJunJulAugSepOctNovDec 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:

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