7.6 Graphs of Sine and Cosine
Example 1:
MATH 162 TRIG
TEAGUE
y = 3cosx
y-intercept = 5
on the interval -x the graph
is increasing: -x0
absolute minimum: -5
-2x2 f(x)=3 x= -2,0,2
x-intercepts 𝑥 =
(2𝑘−1)𝜋
2
𝜋
3𝜋
2
2
= − , 𝜋,
Domain: (-,)
Range: [-5,5]
Example 2: Find the equation of the graph:
Sine function
A = 2 T = 10
2π

2π
10 =
T=

=
2π
10π
=
1
5
1
y = 2sin( x)
5
If you are graphing the sine function you have to choose it in graph tools
This is cosine
Always click reflection FIRST
Example 3:
2π
Find the graph of y=-2cos( x)+3
5
Cosine reflects across x-axis
A=2 and shifts up 3 so add 3 to -2 and 2
2π
T = 2π
T=5
5
One cosine cycle is 0-5
CHECK REFLECTION FIRST