5.1 Using Fundamental Identities
5.1 Using Fundamental Identities
Feb 25, 2016
5.1 Using Fundamental Identities. Fundamental Trigonometric Identities. Fundamental Trigonometric Identities. Co functions. Even or Odd functions. Simplify the Trigonometric Identity . Given: . Simplify the Trigonometric Identity . Given: . Simplify the Trigonometric Identity . Given: . - PowerPoint PPT Presentation
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5.1 Using Fundamental Identities
Fundamental Trigonometric Identities
uu
uu
uu
cot1tan
sec1cos
csc1sin
uu
uu
uu
tan1cot
cos1sec
sin1csc
Fundamental Trigonometric Identities
uuu
uuu
sincoscot
cossintan
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
uuuu
Odd
csc)csc(sinsin
uuuu
Even
sec)sec(cos)cos(
uuuu
Odd
cot)cot(tan)tan(
Simplify the Trigonometric Identity
Given: y
ysin1
cos2
Simplify the Trigonometric Identity
Given:
y
yyy
yy
sin1sin1
sin1cos
sin1cos
2
2
Simplify the Trigonometric Identity
Given:
yyy
yy
yy
yy
2
2
2
2
sin1sin1cos
sin1sin1
sin1cos
sin1cos
Simplify the Trigonometric Identity
Given:
yyy
yy
yy
yy
2
2
2
2
sin1sin1cos
sin1sin1
sin1cos
sin1cos
yy
yy
22
22
sin1cos
1sincos
Simplify the Trigonometric Identity
Given:
yy
yy
yyy
yy
yy
yy
sin1cos
sin1cos
sin1sin1cos
sin1sin1
sin1cos
sin1cos
2
2
2
2
2
2
Simplify the Trigonometric Identity
Given: 1sec1sec2
xx
Simplify the Trigonometric Identity
Given:
1sec
1sec1sec
1sec1sec2
xxx
xx
Simplify the Trigonometric Identity
Given:
1sec
1sec1sec1sec
1sec1sec2
x
xxx
xx
Evaluate the function
Find the six function valuesGiven:
Cot
Tan
Cos
SinFind
553csc;
23sec
Evaluate the function
Find the six function valuesGiven:
25
552
353
2
35
32
553csc;
23sec
Cot
Tan
Cos
Sin
Find
Simplify a Trigonometric expression
Given: SinCscSin
Simplify a Trigonometric expression
Given:
SinSin
SinSin
SinCscSin
21
Simplify a Trigonometric expression
Given:
22
2
2
1
1
CosSinCosSin
SinSinSin
SinSin
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
22
422
422
44
cos116cos1616
)cos4(416
cos2416
cos2;41622
2
22
2
2
2
Using Substitution
Sin
Sin
SinSin
xx
22
422
422
44
cos116cos1616
)cos4(416
cos2416
cos2;41622
2
22
2
2
2
22
21
121
122
2
2
2
2
Cos
Cos
Cos
Cos
Homework
Page 359-361# 1, 17, 27, 37, 47,
53, 57, 65, 77, 87, 93, 107
HomeworkPage 359-361# 10, 26, 36, 48,
54, 58, 68, 78, 88, 94, 120
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