5.1 using fundamental identities. fundamental trigonometric identities
TRANSCRIPT
5.1 Using Fundamental Identities
Fundamental Trigonometric Identities
uu
uu
uu
cot
1tan
sec
1cos
csc
1sin
uu
uu
uu
tan
1cot
cos
1sec
sin
1csc
Fundamental Trigonometric Identities
u
uu
u
uu
sin
coscot
cos
sintan
uu
uu
uu
22
22
22
csccot1
sectan1
1cossin
Co functions
uuuu
uuuu
uuuu
sec2
csc;csc2
sec
tan2
cot;cot2
tan
sin2
cos;cos2
sin
Even or Odd functions
uu
uu
Odd
csc)csc(
sinsin
uu
uu
Even
sec)sec(
cos)cos(
uu
uu
Odd
cot)cot(
tan)tan(
Simplify the Trigonometric Identity
Given: y
y
sin1
cos2
Simplify the Trigonometric Identity
Given:
y
y
y
y
y
y
sin1
sin1
sin1
cos
sin1
cos
2
2
Simplify the Trigonometric Identity
Given:
y
yy
y
y
y
y
y
y
2
2
2
2
sin1
sin1cos
sin1
sin1
sin1
cos
sin1
cos
Simplify the Trigonometric Identity
Given:
y
yy
y
y
y
y
y
y
2
2
2
2
sin1
sin1cos
sin1
sin1
sin1
cos
sin1
cos
yy
yy
22
22
sin1cos
1sincos
Simplify the Trigonometric Identity
Given:
y
y
yy
y
yy
y
y
y
y
y
y
sin1cos
sin1cos
sin1
sin1cos
sin1
sin1
sin1
cos
sin1
cos
2
2
2
2
2
2
Simplify the Trigonometric Identity
Given: 1sec
1sec2
x
x
Simplify the Trigonometric Identity
Given:
1sec
1sec1sec
1sec
1sec2
x
xx
x
x
Simplify the Trigonometric Identity
Given:
1sec
1sec
1sec1sec
1sec
1sec2
x
x
xx
x
x
Evaluate the function
Find the six function values
Given:
Cot
Tan
Cos
Sin
Find
5
53csc;
2
3sec
Evaluate the function
Find the six function values
Given:
2
5
5
52
353
2
3
5
3
2
5
53csc;
2
3sec
Cot
Tan
Cos
Sin
Find
Simplify a Trigonometric expression
Given: SinCscSin
Simplify a Trigonometric expression
Given:
Sin
Sin
SinSin
SinCscSin
21
Simplify a Trigonometric expression
Given:
22
2
2
1
1
CosSin
CosSin
Sin
SinSin
Sin
Sin
SinSin
SinCscSin
Using Substitution
111
1111
111
1
1
22
22
2
23
23
CscxxCotorCscxCscx
CscxxCscuu
uuu
uuu
CscxuSubstitute
CscxxCscxCsc
Using Substitution
Sin
Sin
SinSin
xx
2
2
4
22
422
44
cos116cos1616
)cos4(416
cos2416
cos2;41622
2
22
2
2
2
Using Substitution
Sin
Sin
SinSin
xx
2
2
4
22
422
44
cos116cos1616
)cos4(416
cos2416
cos2;41622
2
22
2
2
2
2
2
2
1
12
1
12
2
2
2
2
2
Cos
Cos
Cos
Cos
Homework
Page 359-361
# 1, 17, 27, 37, 47,
53, 57, 65, 77,
87, 93, 107
Homework
Page 359-361# 10, 26, 36, 48,
54, 58, 68, 78, 88, 94, 120