Good Morning Please have out the following Textbook

Good Morning! Please have out the following: • Textbook (If you have it) • Graphing Whiteboards (If you want it) • Notebook • Pen/Pencil

Graphing Trig Functions

Graphing Trig Functions y = 3 sinx

Graphing Trig Functions y = sin(x+π)

Graphing Trig Functions y = sin(2 x-π)

Question that comes to mind?

The water depth in a narrow channel varies with the tides. The table shows the water depth over a 12 -h period. a. Find a function that models the water depth with respect to time. b. If a boat needs at least 11 ft of water to cross the channel, during which times can it safely do so?

Point of confusion/Hit a wall Write down questions you have Go back to approach Go back to plan Got your questions answered…go Questions didn’t get Was there any relevant Were there any assumptions answered…revise your plan back to execution information you or approximations that missed? Did you contrast the current problem to a previous task/problem? needed to be made? How does the information in the approach inform your plan?

A. Definition Simple Harmonic Motion: repetitive movement back and forth through an equilibrium, or central, position, so that the maximum displacement on one side of this position is equal to the maximum displacement on the other side.

A. Definition Simple Harmonic Motion: the equation that describes the displacement y of an object at time t is y = a sin ωt or y = a cos ωt

A. Definition Simple Harmonic Motion: the equation that describes the displacement y of an object at time t is y = a sin ωt or y = a cos ωt What’s the difference between the period and the frequency?

C. Process A mass suspended from a spring oscillates in simple harmonic motion at a frequency of 4 cycles per second. The distance from the highest to the lowest point of the oscillation is 100 cm. Find an equation that describes the distance of the mass from its rest position as a function of time. Assume that the mass is at its lowest point when t = 0.

D. Purpose: Motion modeled by waves Applications involving harmonic/periodic motion: • sound (middle C) • how light travels • spring/pendulum • Euler’s equation: eix= cosx + isinx. • What happens when you substitute pi in for x? • electricity

Active Practice

Re-visit Task

The water depth in a narrow channel varies with the tides. The table shows the water depth over a 12 -h period. a. Find a function that models the water depth with respect to time. b. If a boat needs at least 11 ft of water to cross the channel, during which times can it safely do so?