Do Now:. 4.5 and 4.6: Graphing Trig Functions Function table: When you first started graphing linear functions you may recall having used the following.

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Presentation transcript:

Do Now:

4.5 and 4.6: Graphing Trig Functions

Function table: When you first started graphing linear functions you may recall having used the following table to graph. x-2012 f(x)

Function Table: We will still pick convenient x values. Our values will be in radians. Lets try the sine function first. x0 sin(x)

Graph y = sin(x): x0 sin(x)0100

Graph of y = sin x Sine graph is periodic (period for y = sin x is ). Five Key Points: Intercepts, Max, and Min. Amplitude = half the distance bet. the max. and min. (amplitude for y = sin x is 1.)

Function Table: We will still pick convenient x values. Our values will be in radians. Lets try the sine function first. x0 cos(x)

Graph y = cos(x): x0 cos(x)1001

Graph of y = cos x Cosine graph is periodic (period for y = cos x is ). Five Key Points: Intercepts, Max, and Min. Amplitude = half the distance bet. the max. and min. (amplitude for y = cos x is 1.)

Graphing: Amplitude = Period = Divide the period by 4 to get four equal subintervals. Phase Shift : solve equations and. This will give you the left and right endpoints of a period. Vertical Shift = The graph of is a reflection in the x-axis of.

Find the period and amplitude of the graph. 1.) 2.) 3.)

Sketch one period of the graph.

Closing: What are the steps for graphing a sin and cosine function?

Homework: Packet 1-14 even; 39, 40,45, 46, 50, 51

Function Table: Lets try the tangent function. x tan(x)

Graph of y = tan x Tangent graph is periodic (period for y = tan x is ). Vertical asymptotes = X-intercepts =

Graphing: Asymptotes = solve equations and. X-intercept: half way between asymptotes. Period = distance between two consecutive asymptotes. The graph of is a reflection in the y-axis of.

Sketch one period of the graph.

table: Fill in the table for cot(x) and compare it to tan(x). x tan(x)

Graph of y = cot x Cotangent graph is periodic (period for y = cot x is ). Vertical asymptotes = X-intercepts =

Graphing: Asymptotes = solve equations and. X-intercept: half way between asymptotes. Period = distance between two consecutive asymptotes. The graph of is a reflection in the y-axis of.

Sketch one period of the graph.

Graphing Cosecant and Secant Cosecant: graph sine first. Where sin x = 0, csc x has a vertical asymptote. Secant: graph cosine first. Where cos x = 0, sec x has a vertical asymptote.

Sketch one period of the graph.

Homework: Worksheet 9 – 29 odd