2. θ cos θ
0 1 2
π 2
4 2
≈0.707
1
π
2 0
3π 2 π π π 3π
4
−
2
≈-0.707 −
3π − 2π
2 2 2 2
-1
π -1
5π 2
4 −
2
≈-0.707 -2
3π
2
0
7π 2
4 2
≈0.707
2π 1

3. y = cos x
Maximum 2 Maximum
1
intercept intercept
-2π -π π 2π
-1
Minimum Minimum
-2

4. y = cos x
Period: the least amount of space (degrees or radians) the function takes
to complete one cycle.
2
1
-2π -π π 2π
-1
-2 Period: 2π

5. y = cos x
How high does it go from its axis?
2
1 Amplitude = 1
-2π -π π 2π
-1
-2

6. y = sin x y = cos x
Try it on your calculator!
2
1
3π π π 3π
−
− 2 2 2
2 -1
-2

7. y = d + a sin (bx - c)
y = d + a cos (bx - c)
a is the amplitude
360° 2π
period = or
b b
c
− is the horizontal translation
b
d is the vertical translation

8. Analyze the graph of y = −3 cos(2πθ + 4π )
amplitude = 3
2π
period = =1
2π
c 4π
horizontal translation: = − =− = −2 (to the left)
b 2π
vertical translation: none

9. Analyze the graph of y = 2 + 3 cos 2 x
amplitude = 3
360°
period = = 180°
2
horizontal translation: none
vertical translation: Up 2

10. y = -2 + 3 cos (2x - 90°) x y
45° 1 high
amplitude = 3
360° 90° -2 mid
period = = 180°
2 135° -5 low
c −90°
horizontal translation:= − = − = 45° 180° -2 mid
b 2
(to the right) 225° 1 high
vertical translation: down 2
1) horiz. tells you 3) divide period by 4 to find
where to start increments
180 ÷ 4 = 45
2) add the period to find table goes in increments of 45
out where to finish
4) plot points and graph
45 + 180 = 225

12.  Analyze the ff. graph of:
1. y = 2 cos(2πθ + 8π )
2. y = −3 + 2 cos(3x + 60°)
3. y = + cos 4x
3 2