Graphing Cosine and Sine Functions Obj: graph sine and cosine on graph paper and notebook paper

 Without any notes, give the following ratios.  sin 135⁰  cos 180⁰  cos 300⁰  sin 150⁰  cos 225⁰  sin 60⁰  QUIZ SOON!!  Get out your unit circle from your notes.

 We can take the circular graph and “unroll” it to graph sin x and cos x on a linear graph.  Check out the x-axis on your graph paper.

 Notice how the x-axis has radian measures from -2π to 2π. You cannot see the increment of π/6, but there is a tick mark for it. Make sure you can locate it on the graph.  The y values are not marked yet. The dotted line above the x-axis is 1 and below the x-axis is -1.

 Now using your circle graph, we are going to take the sine values from the circle and put them on the linear graph.  So start at 0 radians. At 0, the sine value is 0, so put a point at (0, 0) on the linear graph.  Moving around the circle, at π/6, the sine value is ½, so put a point at (π/6, ½).  At π/4, sine is 1/√2. Using your calculator, find an approximation for 1/√2. Plot the point.  Continue around the circle until you have plotted all of the points. Connect the dots.

 The graph has NO sharp points!  The graph has NO straight edges!  This will always be a nice smooth curve.  The max value is 1, the min value is -1. Every value between is on the graph.

 When graphing trig functions without graph paper, ALWAYS label four tick marks on the x-axis and 2 on the y-axis.  Label the x-axis from 0 to 2π and the y-axis from -1 to 1.

 Then put points on the curve at the quadrantal angles. Connect the points with a smooth curve. Remember no sharp points and no straight edges.  It should look like this…

 Find all values of x such that 0 < x < 2π and sin x = 1. X = π/2  Extend your graph on the interval to -2π.  Find 4 values of x such that sin x = 1. x = π/2, 5π/2, -3π/2, -7π/2  Find all values of x such that sin x = 1. x = π/2 + 2πk

 Now graph the cosine values on the graph paper.  Do the same on your notebook paper.  Consider the graph y = sin(x + π/2)

 Sine and cosine are both periodic functions because they conclude one full cycle within a specific period.  What is the period of y = sin x? 2π2π  What is the period of y = cos x? 2π2π  What is the period of your intellectual cycle? emotional? physical?

 In groups of 2 on one sheet of paper, do problems 1 – 4 on page 16. When finished, compare with other 2 in your group. Turn in.  On your own, do problems 7 – 16. These are due next class period.