using the graphing calculator to analyze sinusoidal functions

•Full period examination: Tuesday April 23

•Sine curve & Cosine curve

•Amplitude

•Period

•Range

•Sketching

•Solving sinusoidal equations

•Tides and temperature problems

•Writing the sinusoidal equation

•Topic: Sinusoidal functions
Aim: Using the graphing calculator to analyze the sine and cosine equation

•Do Now:

•Solve the equation in the interval from 0 to 2π. Round your answer to the nearest hundredth:

•2 cos 3Θ = 1.5  

•Solving a cosine equation

Using the graphing calculator,

Y1 = 1.5

Y2 = 2 cos 3Θ  

•Graph both on the same screen

•Window function of the calculator

•Sets up the domain and range and scales units so that you can comfortably see and analyze the solutions of the equation:

•Xmin = 0

•Xmax = 2π

•Xscl = 1

•Ymin = -2

•Ymax = 2

•Yscl = 0.5

•Solving a sinusoidal equation

Use the INTERSECT feature to find the points at which the two graphs intersect.

The graphs show six solutions in the interval

(from 0 to 2π):

They are t ≈ 0.24, 1.85, 2.34, 3.95, 4.43, and 6.04.

These are the solutions of the equation based on the domain from 0 to 2π.

•Group work: Practice 13-5

•Complete Questions # 32, 33 first

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•Then choose any 3 of the circles problems to complete.

•Each question is worth 20 points.

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•This will be counted as an assessment.

•Exit slip

•What are the major differences between the cosine and the sine functions?

•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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