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Do Now:. Algebra II Honors. 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. Function Table:.
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Algebra II Honors 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.
Function Table: • We will still pick convenient x values. Our values will be in radians. Lets try the sine function first.
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.
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.)
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.
Graph of y = tan x • Vertical asymptotes = • X-intercepts = Tangent graph is periodic (period for y = tan x is ).
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 .
table: Fill in the table for cot(x) and compare it to tan(x).
Graph of y = cot x • Vertical asymptotes = • X-intercepts = Cotangent graph is periodic (period for y = cot x is ).
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 .
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.
Homework: • Worksheet • 9 – 29 odd