Sec 1.5
Trig Functions
Def. 1 radian is the measure of a
central angle in the unit circle that cuts out (subtends) an arc with length 1.
when
is in radians
Def: 
and 
Periodic Functions
Period: The smallest value of t to complete 1 cycle.
The 2 functions 
and 
both have a period of 
.
Amplitude: ½ the distance between the minimum and
maximum values of a periodic function.
and both have an amplitude
of 1.
We see that 
The phase shift (horizontal
translation) between and is 
.
Family of sine and cosine functions
Amplitude = 
, Period = 
,
max/min function values A+C , -A+C
shift right by 
for 
, shift left by for 
shift up by 
for 
, shift down by for 
when compared to graph of 
, 
Data: tide chart
|
date |
time |
tide |
Level |
|
4/1/08 |
6
am |
high |
11
ft. |
|
|
12:12
pm |
low |
2
ft. |
|
|
6:24
pm |
High |
11
ft. |
|
4/2/08 |
12:36
am |
low |
2
ft. |
Find the function that outputs tide
level in ft. for an input of time in hours.
Tangent function
For t and number where 
; 
Inverse trig functions
Definition of arcsine: for 
, 
means that
with 
on
Definition of arctangent: for any
value of y , 
means that
with 
on
