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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 .

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Pg. 335 Homework

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  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)

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