Transcript Algebra II Honors

7.6, 7.7 (PC 4.5 & 4.6): Graphing Trig Functions
HW: none
Quiz Friday: 7.6, 7.7
Graph of y = sin x
 Sine graph is periodic (period for y = sin x is 2 ).
 Five Key Points:
Intercepts, Max,
and Min.
 Amplitude = half
the distance bet.
the max. and min.
(amplitude for
y = sin x is 1.)
Graph of y = cos x
 Cosine graph is periodic (period for y = cos x is 2).
 Five Key Points:
Intercepts, Max,
and Min.
 Amplitude = half
the distance bet.
the max. and min.
(amplitude for
y = cos x is 1.)
Graphing:
y  d  a sin(bx  c)
y  d  a cos(bx  c)
 Amplitude = a
2
 Period =
b
 Phase Shift : solve equations bx  c  0 andbx  c  2
 This will give you the left and right endpoints of a period.
 Vertical Shift = d
The graph of y   sin x is a reflection in the x-axis of
y  sin x
Find the period and amplitude of the graph.
1.) y  3 sin x
5
x
2.) y  cos
2
2
2
3.) y  cos x
3
Sketch one period of the graph.
f ( x)  2 sin x
f ( x)  2 cos2 x  3
Sketch one period of the graph.
f ( x)  cos2x


f ( x)  sin x  
4

Sketch one period of the graph.
2
x 
y  cos  
y  3 sin 6 x     2
3
2
4
Graph of y = tan x
 Tangent graph is periodic (period for y = tan xis
 Vertical asymptotes =
 X-intercepts =
n

2
).
 n
Graphing:
y  a tan(bx  c)
 Asymptotes = solve equations
bx  c  

andbx  c 

2
2
 X-intercept: half way between asymptotes.
 Period = distance between two consecutive asymptotes.
The graph of y   tan x is a reflection
in the y-axis of y  tan x.
.
Sketch one period of the graph.
f ( x)  3 tan2 x


f ( x)  2 tan x  
2

Graph of y = cot x
 Cotangent graph is periodic (period for y = cot xis
 Vertical asymptotes = n
 X-intercepts =

2
 n
).
Graphing:
y  a cot(bx  c)
 Asymptotes = solve equationsbx  c  0
andbx  c   .
 X-intercept: half way between asymptotes.
 Period = distance between two consecutive asymptotes.
The graph of y   cot x is a reflection
in the y-axis of y  cot x.
Sketch one period of the graph.
x
f ( x )  2 cot
3
 x  
f ( x)  0.1cot  
 4 4
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.
f ( x)  sec 2 x


f ( x)  2 csc x  
4

Sketch one period of the graph.
x
f ( x)  csc
2
1
f ( x)  sec 2 x   
2