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Graphs of Trigonometry Functions, Schemes and Mind Maps of Trigonometry

San Juan Basin Technical College 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 𝑓𝑓(𝑥𝑥)=sin (𝑥𝑥)

Domain: (−∞,∞)

Range:

[−1, 1]

Odd/Even: Odd

Period:

2𝜋𝜋

Cosine 𝑓𝑓(𝑥𝑥)=cos (𝑥𝑥)

Domain: (−∞,∞)

Range:

[−1, 1]

Odd/Even: Even

Period:

2𝜋𝜋

Tangent

𝑓𝑓(𝑥𝑥)=tan(𝑥𝑥)

=sin (𝑥𝑥)

cos (𝑥𝑥)

Domain: (−∞,∞) except for

𝑥𝑥=𝜋𝜋

2

±𝑛𝑛𝜋𝜋

Range: (−∞,∞)

Odd/Even: Odd

Period: 𝜋𝜋

Asymptotes at

𝑥𝑥=

𝜋𝜋

2±𝑛𝑛𝜋𝜋

Cosecant

𝑓𝑓(𝑥𝑥)=csc(𝑥𝑥)

=1

sin (𝑥𝑥)

Domain: (−∞,∞) except for

𝑥𝑥= ±𝑛𝑛𝜋𝜋

Range: (−∞,−1]∪[1, ∞)

Odd/Even: Odd

Period: 2𝜋𝜋

Secant

𝑓𝑓(𝑥𝑥)=sec(𝑥𝑥)

=1

cos (𝑥𝑥)

Domain: (−∞,∞) except for

𝑥𝑥=𝜋𝜋

2

±𝑛𝑛𝜋𝜋

Range: (−∞,−1]∪[1, ∞)

Odd/Even: Even

Period: 2𝜋𝜋

Cotangent

𝑓𝑓(𝑥𝑥)=cot(𝑥𝑥)

=1

tan(𝑥𝑥)

=cos(𝑥𝑥)

sin(𝑥𝑥)

Domain: (−∞,∞) except for

𝑥𝑥= ±𝑛𝑛𝜋𝜋

Range: (−∞,∞)

Odd/Even: Odd

Period: 𝜋𝜋

Asymptotes at

𝑥𝑥= ±𝑛𝑛𝜋𝜋

General Form: 𝑓𝑓(𝑥𝑥)=𝑎𝑎sin[𝑏𝑏(𝑥𝑥 − ℎ)]+𝑘𝑘 *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 𝑓𝑓

) = sin( 𝑥𝑥)

Domain: (−∞, ∞)

Range:

[

]

Odd/Even: Odd

Period: 2 𝜋𝜋

Cosine 𝑓𝑓

) = cos( 𝑥𝑥)

Domain:

Range: [− 1 , 1 ]

Odd/Even: Even

Period: 2 𝜋𝜋

Tangent

= tan

sin(𝑥𝑥)

cos(𝑥𝑥)

Domain: (−∞, ∞) except for

𝜋𝜋

2

Range: (−∞, ∞)

Odd/Even: Odd

Period: 𝜋𝜋

Asymptotes at 𝑥𝑥 =

𝜋𝜋

2

Cosecant

𝑓𝑓(𝑥𝑥) = csc(𝑥𝑥)

sin(𝑥𝑥)

Domain: (−∞, ∞) except for

Range:

−∞, −1]

[1,

Odd/Even: Odd

Period: 2 𝜋𝜋

Secant

𝑓𝑓(𝑥𝑥) = sec(𝑥𝑥)

cos(𝑥𝑥)

Domain:

except for

𝜋𝜋

2

Range:

−∞, −1]

[1,

Odd/Even: Even

Period: 2 𝜋𝜋

Cotangent

= cot

tan(𝑥𝑥

cos(𝑥𝑥)

sin(𝑥𝑥)

Domain: (−∞, ∞) except for

Range:

Odd/Even: Odd

Period: 𝜋𝜋

Asymptotes at 𝑥𝑥 = ±𝑛𝑛𝜋𝜋

General Form: 𝑓𝑓(𝑥𝑥) = 𝑎𝑎 sin[𝑏𝑏(𝑥𝑥 − ℎ)] + 𝑘𝑘 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

−

= arcsin(𝑥𝑥)

Domain: [−1,1]

Range: �

−𝜋𝜋

2

𝜋𝜋

2

Inverse

Cosine

𝑓𝑓(𝑥𝑥) = cos

−

= arccos(𝑥𝑥)

Domain:

[

−1,1]

Range: [0, 𝜋𝜋]

Inverse

Tangent

) = tan

−

= arctan(𝑥𝑥)

Domain: (−∞, ∞)

Range: �

−𝜋𝜋

2

𝜋𝜋

2

Inverse

Cosecant

𝑓𝑓(𝑥𝑥) = csc

−

= arccsc(𝑥𝑥)

Domain: (−∞, − 1 ] ∪ [ 1 , ∞)

Range: �

−𝜋𝜋

2

𝜋𝜋

2

Inverse

Secant

𝑓𝑓(𝑥𝑥) = sec

−

= arcsec(𝑥𝑥)

Domain:

]

[

Range: [0, 𝜋𝜋], 𝑦𝑦 ≠

𝜋𝜋

2

Inverse

Cotangent

) = cot

−

= arccot(𝑥𝑥)

Domain: (−∞, ∞)

Range: (0, 𝜋𝜋)

Graphs of Trigonometry Functions, Schemes and Mind Maps of Trigonometry

Related documents

Partial preview of the text

Download Graphs of Trigonometry Functions and more Schemes and Mind Maps Trigonometry in PDF only on Docsity!

Graphs of Trigonometry Functions

Function

Name

Parent

Function

Graph of Function Characteristics

[

]

−∞, −1]

[1,

−∞, −1]

[1,

Graphs of Inverse Trigonometry Functions

Function

Name

Parent

Function

Graph of Function Characteristics

[

−1,1]

]

[