Download Is this an even or odd function?

January 19th
in your BOOK, 4.2
copyright2009merrydavidson
Special Right Triangles
S O H C A H T O A
S O H C A H T O A
hyp

opp
opp

hyp
adj

hyp
hyp

adj
opp

adj
adj

opp
r
Parent functions

x
y
Reciprocal functions
Reciprocal Identities
Memorize these 11 identities
for a quiz SOON!!!
Look at your unit circle now…
sine
cosine
Check out the
Pythagorean Identities
Evaluating Trig Functions:
Use your Plate, find the angle, evaluate.
Rationalize the denominator as needed.
1: Find the six trig. values for 300.
sin 300o =
cos 300o =
tan 300o =
3

2
1
2
 3
csc 300o =  2 3
3
sec 300o =
2
cot 300o =
3

3
Evaluating Trig Functions:
Use your Plate, find the angle, evaluate.
Rationalize the denominator as needed.
2: Find the six trig. values for -5/4.
sin 5 =
csc 5 = 2 2  2
2
4
5
cos
=

4
5
tan
4 =
4
2
2
2
1
2
5
2
2
sec
=
 2
2
4
5
cot
4
= 1
Find the sine of the angles listed.
1
1
1
o
o
o
30 =
390 =
-330 =
2
2
2
What is the NAME of the type of
these 3 angles? co-terminal angles
What conclusion can you make?
Co-terminal angles have the same
trig values.
It takes 360o to get to the same trig
value, thus the PERIOD for the sine
and cosecant function is 360o2 radians
Find the cosine of the angles listed.
1
1
1
o
o
o
60 =
420 =
-300 =
2
2
2
It takes 360o to get to the same
place, thus the PERIOD for the
cosine and secant function is 360o
or 2 radians .
Find the tangent of the angles listed.
45o =
225o = 1
-135o =
1
It takes 180o to get the same trig
value, thus the PERIOD for the
tangent and cotangent function is
180o  radians .
1
Summary of Period
sin/csc/cos/sec have a period of 360o
2 radians .
tan/cot have a period of 1800
 radians
BE CAREFUL TO NOT USE CAPITAL
LETTERS. WE WILL LEARN THAT
LATER
.
Is this an even or odd function?
y = sin x
y = csc x is also odd.
y = sec x
is also
even
y = cos x










Is this an even or odd function?

y = tan x
y = cot x is also odd


-360
-270

-180
-90

0
90

180
Is this an even or odd function?
270

360
Now look at the
even/odd Identities
What does this mean????
Trig Identities
f(x) = cos x
EVEN
cos   x   cos x
sec   x   sec x
f(x) = sin x
ODD
sin   x    sin x
csc   x    csc x
cos   x   cos x
sec   x   sec x
sin   x    sin x
Problemscsc   x    csc x
1) If sin (t) = ¼, find sin (-t).
-1/4
2) If sin (t) is 3/8, find csc (-t).
If sin (t) is 3/8, then csc (t) = 8/3.
We want to find csc (-t) which is the
opposite of csc (t) = -8/3.
3) If cos (t) = -3/4, find cos(-t).
cos(t) = cos(-t) so = -3/4
Trig Identities
f(x) = tan x
ODD
tan   x    tan x
cot   x    cot x
If tan (t) = 2/3
find tan (-t).
-2/3
HW: WS 6-4