•Topic: Sinusoidal functions
Aim: How can we create a cosine equation modeling a “tide” problem?
Aim: How can we create a cosine equation modeling a “tide” problem?
•Do Now:
•If y = -2 cos Θ
•What
is the amplitude and period of the function?
•Sketching
a cosine graph
•Identify
amplitude
•Identify
the cycle, b
•Use
period = 2π/b
•Draw
the xy plane and label your axes
•Decide
on the units for each axis and label
•Identify
and plot the 5 point summary
•Connect
the points and voila !!!
•Tides
•Average
depth = 5.5 ft
•Amplitude
= 1.5 ft
•12
hr and 22 min for one cycle
•Y
= 1.5 cos 60π/371 t
•Suppose
your boat needs at least 5 ft of
water to approach or leave the pier,
what equation would model this situation?
Can
you find these times?
•In
class assessment
•Complete
problems 10, 11, 18, 19, 21, 27 and 30 on the handout.
•Page
857 circled problems
•All
questions should be answered on separate sheet of paper with your name clearly
displayed
•Hand
in before the bell rings
•Exit slip
•What
are the solutions to the following equation in the interval from 0 to 2π?
•-2
cos
Θ
= -1.2
•Answer
to the DNA question
•Because
one cos curve is drawn from 0 to 24
(x-axis), the period of the curve is 24.
•Using
the formula y = a cos
bx, we
can find a = 1 (amplitude) and b = π/12 (because period = 2π/b, so 24 = 2π/b,
making b = π/12.)
•Therefore,
y = 1cos (π/12)x or simply y = cos
(π/12)x .
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