Presentation on theme: "GRAPHING TRIGONOMETRIC FUNCTIONS"— Presentation transcript:
1 GRAPHING TRIGONOMETRIC FUNCTIONS Using the TI-83+ ™
2 GRAPHING BASIC TRIGONOMETRIC FUNCTIONS Setting up the calculator.Graphing the sine and cosine functions.Graphing the tangentfunction.Graphing the reciprocal trig functions.
3 Setting Up the Calculator Press the Mode key.Select the appropriate mode.Press Window key.Choose your x-min value and x-max value.Use the “pi” or “π” key when appropriate.Set your x-scale by using ¼ of the length of the period.
4 Graphing Sine and Cosine Curves in the form: y= a sin(bx) y =a cos(bx) Choosing the Ymin and Ymax values depends on the amplitude. Find the amplitude, l a l.It is recommended to select a Ymin at least one value lower than your amplitude (plus the phase shift) and to select a Ymax at least one value higher than that value. Select an appropriate y-scl based on the size of your amplitude. A “1” value will probably be sufficient.Leave Xres = 1.
5 Viewing the Graph Press the y= key. Check to be sure the “Plot 1” key is not highlighted.Enter the equation under Y1=.Press the graph key.
6 SAMPLE GRAPH: y= 3 sin(2x) For y = 3 sin (2x), the amplitude = 3 and the period is (2π)/2 or π.Setting The Window:In order to graph 2 full cycles, set the Xmin at –π and the Xmax at π.Since the period is π, the Xscl should be ¼ of π, or π/4.Since the amplitude is 3, set the Ymin = -4, the Ymax = 4, and Yscl=1.Enter the equation in Y1=ππ
7 Graphing the tangent curve in the form of y = a tan (bx) The window setting for x min and x max should be set according to the number of cycles desired. Again, the x sc l should be set to ¼ of the period. Recall the period of the tangent function is π/ lblSince the tangent function has no upper and lower limit, choose a reasonable y min and y max value for the window setting. Be sure to include values at least from a to –a.
8 SAMPLE GRAPH: y = 2 tan xFor y = 2 tan x, a = 2 and the period is π/1, or π.Setting the window:Since the period is π, the Xmin should be set at –π, the Xmax is π, and the Xscl should be set to π/4.Since a =2, set the Ymin to -5, Ymax to 5, and the Yscl to 1.Enter the equation in Y1=.
9 GRAPHING THE RECIPROCAL FUNCTIONS In order to graph the reciprocal trig functions, use the reciprocal key x-1 with either the sin, cos, or tan key.
10 SAMPLE PROBLEM: y = 2sec x Since the secant is the reciprocal of cosine, consider the graph of y = 2 cos x when setting the Xmin, Xmax and Xscl on the window. Since the period is 2π, set the xscl:Xmin= -2π Xmax = 2π Xscl =π/2Since the secant has no limit, set the Ymin lower than –l a l and Ymax higher than la l.Ymin=- 6 and Ymax = 6.Enter the equation in Y1=.
11 The graph of y = 2 sec xThe graph of y = 2 sec x is shown here. Do you see the asymptotes? Are there any x or y- intercepts?
12 Now, try these! Graph at least two cycles. y = 3 csc 4x.y = 5 cot 2x.y = 2 cos ¼x.y = -4 sin πxy = ½ tan x.y = -3 sec x/2