1 / 6

Pg. 335 Homework

Pg. 335 Homework. Pg. 346 #1 – 14 all, 21 – 26 all Study Trig Info!! #45 #46 #47 #48 #49 Proof #50 Proof #51 + , + , + #52 + , – , – #53 – , – , + #54 – , + , – #55 #56 . 6.3 Graphs of sin x and cos x. The Unit Circle. The graph of sin x .

vega
Télécharger la présentation

Pg. 335 Homework

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. Pg. 335 Homework • Pg. 346 #1 – 14 all, 21 – 26 allStudy Trig Info!! • #45 #46 • #47 #48 • #49 Proof #50 Proof • #51 + , + , + #52 + , – , – • #53– , –, + #54 –, +, – • #55 #56

  2. 6.3 Graphs of sin x and cosx The Unit Circle The graph of sin x. The graph of cosx. • The Unit Circle can help us graph each individual function of sin x and cosx by looking at the unique output values for each input value. This gives us a domain and range. • Look at your Unit Circle. What do you notice about the input and output values?

  3. 6.3 Graphs of sin x and cosx sin x and cos x together Where do the maximums and minimums of the graphs occur? What is the domain? Range? Graph: y = sin xy = 2sin xy = 3sin xIn the same window. What do you notice? • Where do they intersect?How do you know?

  4. 6.3 Graphs of sin x and cosx Amplitude Period Length Graph: y = sin xy = sin (4x)y = sin (0.5x)In the same window. What do you notice? One period length of y = sin bx or y = cosbx is • Graph: y = cosxy = -2cos xIn the same window. What do you notice? • The amplitude of f(x) = asinx and f(x) = acos x is the maximum value of y, where a is any real number; amplitude = |a|.

  5. 6.3 Graphs of sin x and cosx Horizontal Shifts Symmetry of sin x and cosx Looking at the Unit Circle to help, think about the difference between the following: sin (-x) = -sin (x) cos (-x) = cos (x) • Remember our cofunctions and why they were true? Well, they are true with graphing too! • The cofunctions lead into shifts. If a value is inside with the x, it is a horizontal shift left or right opposite the sign. If it is outside the trig, it is up or down as the sign states.

  6. 6.3 Graphs of sin x and cosx Examples  Graph the following: Solve for the following: sin x = 0.32 on 0 ≤ x < 2π cosx = -0.75 on 0 ≤ x < 2π sin x = -0.14 on 0 ≤ x < 2π cosx = 0.65 on 0 ≤ x < 2π • y = 4sin x • y = -3cos (2x) • y = sin (0.5x) + 1 • y = 2sin (x – 1)

More Related