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Homework

Homework. Pg. 385 # 9, 10, 35 – 38, 43 , 44, 46, 51 (on the last 4, use calculator to rewrite as a sinusoid) Memorization quiz on Thursday!!. 7.1 Transformations and Trigonometric Graphs. Review of Transformations. Sinusoids.

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Homework

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  1. Homework • Pg. 385 #9, 10, 35 – 38, 43, 44, 46, 51 (on the last 4, use calculator to rewrite as a sinusoid)Memorization quiz on Thursday!!

  2. 7.1 Transformations and Trigonometric Graphs Review of Transformations Sinusoids A sinusoid is a function that can be written in the formf(x) = asin(bx + c) + dwhere a, b, c, and d are real numbers. The graph of a sinusoid can be obtained from the graph of y = sin x by a combination of horizontal stretching or shrinking, horizontal shifting, vertical stretching or shrinking and vertical shifting. • If y = f(x) is the original graph, what do the following do? • y = af(x) • y = -f(x) • y = f(x + c) • y = f(x – c) • y = f(x) + d • y = f(x) – d • y = f(-x)

  3. 7.1 Transformations and Trigonometric Graphs Sums that are Sinusoidal Practicing Sinusoids Show that f(x) = 2sin x + 5cos xis a sinusoid.Also, approximate A and α so that Asin (x + α) = 2sin x + 5cos x • For all real numbers a and b, the functionf(x) = asinx + bcosxis a sinusoid. In particular, there exist real numbers A and α such thatasinx + bcosx = Asin (x + α),where |A| is the amplitude and α is the phase shift.

  4. 7.1 Transformations and Trigonometric Graphs Sums that are Sinusoidal Practicing Sinusoids Show that f(x) = 3sin (2x – 1) + 4cos (2x + 3) is a sinusoid. Also, approximate A and α so that Asin (2x + α) = 3sin (2x – 1) + 4cos (2x + 3) • For all real numbers a, b, d, h, k the functionf(x) = asin (bx + h) + dcos (bx+ k) is a sinusoid. In particular, there exist real numbers A and α such thatasin (bx + h) + dcos (bx+ k) = Asin (bx + α)

  5. 7.1 Transformations and Trigonometric Graphs Practicing Sinusoids Decide which of the following are sinusoids. If f(x) is a sinusoid, determine A and α. • Show that f(x) = sin (2x) + cos (3x) is not sinusoidal. Also, find the domain, range, and period of f.

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