1. TRIGONOMETRY UNIT 2:
By: Crystal Quintero
May 2013 Period 1

2. GRAPHING PROPERTIES: AMPLITUDE,
FREQUENCY, PERIOD, PHASE SHIFT
• Amplitude is half the distance between the minimum and maximum value of
the range of a periodic function with a bounded range. lAl
• Frequency is how often something happens. lbl/2pi
• Period is the time of completion. 2pi/lbl
• Phase shift is h (y=asin(b(x-h))+k

3. EXAMPLES:
Y=4cos3x
• Amplitude=lAl=l4l=4
• Period=2pi/lbl=2pi/l3l=2pi/3
• Frequency=lbl/2pi=l3l/2pi=3/2pi
• Phase Shift: h=0
Y=-2sin2x
• Amplitude=l-2l=2
• Period=2pi/2=pi
• Frequency=2/2pi=1/pi
• Phase Shift=0

4. TRIGONOMETRIC FUNCTION AND
ITS INVERSE WITH THE UNIT CIRCLE
Inverse Sine Function
• Y=sin-1x or xsiny
• Range: [-1, 1]
• Domain: [-pi/2, pi/2]

5. INVERSE COSINE FUNCTION
•Y=cos-1x or x=cosy
•Domain: [-1, 1]
•Range: [0, pi]

6. INVERSE TANGENT
FUNCTION
• Y=tan-1x or x=tanyy
• Domain: [-∞, ∞]
• Range: [-pi/2, pi/2]

7. EXAMPLES
• Sin-1(1/2)=/6
• (√3/2, ½)
• Cos-1(1/2)=/3
• (1/2, √3,2)
• Tan-1(√3)=/3
• (1/2, √3,2)

8. STUDENTS USE TRIGONOMETRY IN
A VARIETY OF WORD PROBLEMS
• A math student is standing 25 feet
from the base of the Washington
Monument. The angle of elevation
from her horizontal line of sight
is 87.4 degrees. If her “eye height” is
5 ft, how tall is the monument?