1 / 5

How’d the test go?!?

This text provides a comprehensive review of sinusoidal functions and their transformations. It discusses how sinusoids can be represented in the form f(x) = a sin(bx + c) + d, where a, b, c, and d are real numbers. It explains how to obtain the graph of a sinusoid from the basic y = sin x function through various stretching, shifting, and transformations. Additionally, it includes examples to demonstrate that certain combinations of sine and cosine functions can also be expressed as sinusoids, and outlines the process for determining amplitude and phase shifts.

stuart
Télécharger la présentation

How’d the test go?!?

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. How’d the test go?!? • Pg. 385 #43,44, 46, 51 (use calculator to rewrite as a sinusoid) #9, 10, 35-38 allMemorization quiz through inverse trig functions on Friday!!

  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.

More Related