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Graphs of Trigonometry Functions, Schemes and Mind Maps of Trigonometry

Mohawk Valley Community College. Learning Commons Math Lab IT129. Function. Name. Parent. Function. Graph of Function. Characteristics. Sine.

Typology: Schemes and Mind Maps

2021/2022

Uploaded on 09/12/2022

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Graphs of Trigonometry Functions
Mohawk Valley Community College Learning Commons Math Lab IT129
Function
Name
Parent
Function
Graph of Function
Characteristics
Sine ๐‘“๐‘“(๐‘ฅ๐‘ฅ)=sin (๐‘ฅ๐‘ฅ)
Domain: (โˆ’โˆž,โˆž)
Range:
[โˆ’1, 1]
Odd/Even: Odd
Period:
2๐œ‹๐œ‹
Cosine ๐‘“๐‘“(๐‘ฅ๐‘ฅ)=cos (๐‘ฅ๐‘ฅ)
Domain: (โˆ’โˆž,โˆž)
Range:
[โˆ’1, 1]
Odd/Even: Even
Period:
2๐œ‹๐œ‹
Tangent
๐‘“๐‘“(๐‘ฅ๐‘ฅ)=tan(๐‘ฅ๐‘ฅ)
=sin (๐‘ฅ๐‘ฅ)
cos (๐‘ฅ๐‘ฅ)
Domain: (โˆ’โˆž,โˆž) except for
๐‘ฅ๐‘ฅ=๐œ‹๐œ‹
2
ยฑ๐‘›๐‘›๐œ‹๐œ‹
Range: (โˆ’โˆž,โˆž)
Odd/Even: Odd
Period: ๐œ‹๐œ‹
Asymptotes at
๐‘ฅ๐‘ฅ=
๐œ‹๐œ‹
2ยฑ๐‘›๐‘›๐œ‹๐œ‹
Cosecant
๐‘“๐‘“(๐‘ฅ๐‘ฅ)=csc(๐‘ฅ๐‘ฅ)
=1
sin (๐‘ฅ๐‘ฅ)
Domain: (โˆ’โˆž,โˆž) except for
๐‘ฅ๐‘ฅ= ยฑ๐‘›๐‘›๐œ‹๐œ‹
Range: (โˆ’โˆž,โˆ’1]โˆช[1, โˆž)
Odd/Even: Odd
Period: 2๐œ‹๐œ‹
Secant
๐‘“๐‘“(๐‘ฅ๐‘ฅ)=sec(๐‘ฅ๐‘ฅ)
=1
cos (๐‘ฅ๐‘ฅ)
Domain: (โˆ’โˆž,โˆž) except for
๐‘ฅ๐‘ฅ=๐œ‹๐œ‹
2
ยฑ๐‘›๐‘›๐œ‹๐œ‹
Range: (โˆ’โˆž,โˆ’1]โˆช[1, โˆž)
Odd/Even: Even
Period: 2๐œ‹๐œ‹
Cotangent
๐‘“๐‘“(๐‘ฅ๐‘ฅ)=cot(๐‘ฅ๐‘ฅ)
=1
tan(๐‘ฅ๐‘ฅ)
=cos(๐‘ฅ๐‘ฅ)
sin(๐‘ฅ๐‘ฅ)
Domain: (โˆ’โˆž,โˆž) except for
๐‘ฅ๐‘ฅ= ยฑ๐‘›๐‘›๐œ‹๐œ‹
Range: (โˆ’โˆž,โˆž)
Odd/Even: Odd
Period: ๐œ‹๐œ‹
Asymptotes at
๐‘ฅ๐‘ฅ= ยฑ๐‘›๐‘›๐œ‹๐œ‹
General Form: ๐‘“๐‘“(๐‘ฅ๐‘ฅ)=๐‘Ž๐‘Žsin[๐‘๐‘(๐‘ฅ๐‘ฅ โˆ’ โ„Ž)]+๐‘˜๐‘˜ *This general form can be used for any trigonometric function*
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Graphs of Trigonometry Functions

Mohawk Valley Community College Learning Commons Math Lab IT

Function

Name

Parent

Function

Graph of Function Characteristics

Sine ๐‘“๐‘“

) = sin( ๐‘ฅ๐‘ฅ)

Domain: (โˆ’โˆž, โˆž)

Range:

[

]

Odd/Even: Odd

Period: 2 ๐œ‹๐œ‹

Cosine ๐‘“๐‘“

) = cos( ๐‘ฅ๐‘ฅ)

Domain:

Range: [โˆ’ 1 , 1 ]

Odd/Even: Even

Period: 2 ๐œ‹๐œ‹

Tangent

= tan

sin(๐‘ฅ๐‘ฅ)

cos(๐‘ฅ๐‘ฅ)

Domain: (โˆ’โˆž, โˆž) except for

๐œ‹๐œ‹

2

Range: (โˆ’โˆž, โˆž)

Odd/Even: Odd

Period: ๐œ‹๐œ‹

Asymptotes at ๐‘ฅ๐‘ฅ =

๐œ‹๐œ‹

2

Cosecant

๐‘“๐‘“(๐‘ฅ๐‘ฅ) = csc(๐‘ฅ๐‘ฅ)

sin(๐‘ฅ๐‘ฅ)

Domain: (โˆ’โˆž, โˆž) except for

Range:

โˆ’โˆž, โˆ’1]

[1,

Odd/Even: Odd

Period: 2 ๐œ‹๐œ‹

Secant

๐‘“๐‘“(๐‘ฅ๐‘ฅ) = sec(๐‘ฅ๐‘ฅ)

cos(๐‘ฅ๐‘ฅ)

Domain:

except for

๐œ‹๐œ‹

2

Range:

โˆ’โˆž, โˆ’1]

[1,

Odd/Even: Even

Period: 2 ๐œ‹๐œ‹

Cotangent

= cot

tan(๐‘ฅ๐‘ฅ

cos(๐‘ฅ๐‘ฅ)

sin(๐‘ฅ๐‘ฅ)

Domain: (โˆ’โˆž, โˆž) except for

Range:

Odd/Even: Odd

Period: ๐œ‹๐œ‹

Asymptotes at ๐‘ฅ๐‘ฅ = ยฑ๐‘›๐‘›๐œ‹๐œ‹

General Form: ๐‘“๐‘“(๐‘ฅ๐‘ฅ) = ๐‘Ž๐‘Ž sin[๐‘๐‘(๐‘ฅ๐‘ฅ โˆ’ โ„Ž)] + ๐‘˜๐‘˜ This general form can be used for any trigonometric function

Graphs of Inverse Trigonometry Functions

Mohawk Valley Community College Learning Commons Math Lab IT

Function

Name

Parent

Function

Graph of Function Characteristics

Inverse Sine

) = sin

โˆ’

= arcsin(๐‘ฅ๐‘ฅ)

Domain: [โˆ’1,1]

Range: ๏ฟฝ

โˆ’๐œ‹๐œ‹

2

๐œ‹๐œ‹

2

Inverse

Cosine

๐‘“๐‘“(๐‘ฅ๐‘ฅ) = cos

โˆ’

= arccos(๐‘ฅ๐‘ฅ)

Domain:

[

โˆ’1,1]

Range: [0, ๐œ‹๐œ‹]

Inverse

Tangent

) = tan

โˆ’

= arctan(๐‘ฅ๐‘ฅ)

Domain: (โˆ’โˆž, โˆž)

Range: ๏ฟฝ

โˆ’๐œ‹๐œ‹

2

๐œ‹๐œ‹

2

Inverse

Cosecant

๐‘“๐‘“(๐‘ฅ๐‘ฅ) = csc

โˆ’

= arccsc(๐‘ฅ๐‘ฅ)

Domain: (โˆ’โˆž, โˆ’ 1 ] โˆช [ 1 , โˆž)

Range: ๏ฟฝ

โˆ’๐œ‹๐œ‹

2

๐œ‹๐œ‹

2

Inverse

Secant

๐‘“๐‘“(๐‘ฅ๐‘ฅ) = sec

โˆ’

= arcsec(๐‘ฅ๐‘ฅ)

Domain:

]

[

Range: [0, ๐œ‹๐œ‹], ๐‘ฆ๐‘ฆ โ‰ 

๐œ‹๐œ‹

2

Inverse

Cotangent

) = cot

โˆ’

= arccot(๐‘ฅ๐‘ฅ)

Domain: (โˆ’โˆž, โˆž)

Range: (0, ๐œ‹๐œ‹)