Below are a series of videos showing how to graph the since function.
Videos 1-11 all have functions where the period is 2π. Videos 12-20 have a different period.
Graph Sine Function 1: http://youtu.be/DaCK1O-fcO0
Intro and Graph function in form y = sin(x): y = sin(x)
Graph Sine Function 2: http://youtu.be/0mSOwzvXaHw
Graph functions in form y = Asin(x); Domain, Range, Amplitude: y = sin(x)
Graph Sine Function 3: http://youtu.be/m4I7xF81mpk
Graph functions in form y = Asin(x); Domain, Range, Amplitude: 2sin(x); y = 3sin(x); y = (1/2)sin(x)
Graph Sine Function 4: http://youtu.be/H13jkI7dPbo
Graph functions in form y = Asin(x); Domain, Range, Amplitude; y = —3sin(x); y = (1/3)sin(x)
Graph Sine Function 5: http://youtu.be/TrF4Ox2wCTk
Vertical translation of sine function; Graph functions in form y = sin(x) + D; Domain, Range, Amplitude: y = sin(x) + 1; y = sin(x) — 3
Graph Sine Function 6: http://youtu.be/yVOPNnWeJNA
Vertical translation and stretch of sine function; Graph functions in form y = Asin(x) + D; Domain, Range, Amplitude: y = 5sin(x) — 2; y = —sin(x) + 1
Graph Sine Function 7: http://youtu.be/bwF6NmXy2II
Phase Shift of sine function; Graph functions in form y = sin(x + C): y = sin(x + π/4)
Graph Sine Function 8: http://youtu.be/-5gNNeKcMng
Phase Shift of sine function; Graph functions in form y = sin(x + C): y = sin(x — π/3)
Graph Sine Function 9: http://youtu.be/BXWqqUX2oO0
Phase Shift of sine function; Graph functions in form y = Asin(x + C): y = —2sin(x + 5π/6)
Graph Sine Function 10: http://youtu.be/MN32FVtmL14
Graph of functions with Phase Shift and vertical shift of sine function; Graph functions in form y = sin(x + C) + D; y = sin(x—π/2) + 3
Graph Sine Function 11: http://youtu.be/CzbPTw8dnAo
Graph of function with Phase Shift and vertical shift and amplitude of sine function; Graph functions in form y = Asin(x + C) + D; y = 3sin(x + π/6) — 1
Below are videos where the period is not 2π, so these go along with section 2.2 in the book.
Graph Sine Function 12: http://youtu.be/T8AIdTZq9-Q
Covers how to find the period of a sine function and graph it; Graph and find period of y=sin(2x)
Graph Sine Function 13: http://youtu.be/y-_e00reJBA
Video is second part of video on finding the period of function; find period of y=sin(2x); y=sin(3x/4); y=sin(bx); y=sin(3x); y=sin(x/2)
Graph Sine Function 14: http://youtu.be/kF8hlhT7QmA
Video goes over how to find the period and graph a function having a period different that 2π; y = sin(3x)
Graph Sine Function 15: http://youtu.be/oHCfZdHuorY
Video goes over a function having an amplitude other than 1 and period different that 2π; y = 2sin(x/4)
Graph Sine Function 16: http://youtu.be/Jl5DpBI3c3g
Video goes over a function having an amplitude other than 1 and period different that 2π; y = (—1/2)sin[(π/3)x]
Graph Sine Function 17: http://youtu.be/USF6x_iTdzU
Video goes over a function having a period different that 2π, and a vertical shift; y = sin(2x) — 3
Graph Sine Function 18: http://youtu.be/tpuNpbZM__M
Video goes over a function having a period different that 2π, and a vertical shift, as well as a reflection; y = —sin(3x/2)
Graph Sine Function 19: http://youtu.be/4MMp3F8U1fw
Video goes over a function having an amplitude other than 1 and period different that 2π, as well as a phase shift; y = (1/3)sin(2x + π)
Graph Sine Function 20: http://youtu.be/LFF6xRGwb6Q
Video goes over a function having an amplitude other than 1, a vertical shift, and period different that 2π, as well as a phase shift; y = 4sin(3x — π/2)