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

6.3 Graphs of sin x and cos x The Unit Circle The Unit Circle can help us graph each individual function of sin x and cos x 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? The graph of sin x. The graph of cos x.

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

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

6.3 Graphs of sin x and cos x Horizontal Shifts 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. Symmetry of sin x and cos x Looking at the Unit Circle to help, think about the difference between the following: sin (-x) = -sin (x) cos (-x) = cos (x)

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