Graphs of Trigonometry Functions
Function
Name
Sine
Cosine
Tangent
Cosecant
Secant
Parent
Function
𝑓𝑓(𝑥𝑥) = sin(𝑥𝑥)
𝑓𝑓(𝑥𝑥) = cos(𝑥𝑥)
𝑓𝑓(𝑥𝑥) = tan(𝑥𝑥)
=
sin(𝑥𝑥)
cos(𝑥𝑥)
Characteristics
Domain: (−∞, ∞)
Range: [−1, 1]
Odd/Even: Odd
Period: 2𝜋𝜋
Domain: (−∞, ∞)
Range: [−1, 1]
Odd/Even: Even
Period: 2𝜋𝜋
Domain: (−∞, ∞) except for
𝜋𝜋
𝑥𝑥 = ± 𝑛𝑛𝑛𝑛
2
Range: (−∞, ∞)
Odd/Even: Odd
Period: 𝜋𝜋
𝜋𝜋
Asymptotes at 𝑥𝑥 = 2 ± 𝑛𝑛𝑛𝑛
𝑓𝑓(𝑥𝑥) = csc(𝑥𝑥)
Domain: (−∞, ∞) except for
𝑥𝑥 = ±𝑛𝑛𝑛𝑛
Range: (−∞, −1] ∪ [1, ∞)
Odd/Even: Odd
Period: 2𝜋𝜋
𝑓𝑓(𝑥𝑥) = sec(𝑥𝑥)
Domain: (−∞, ∞) except for
𝜋𝜋
𝑥𝑥 = ± 𝑛𝑛𝑛𝑛
2
Range: (−∞, −1] ∪ [1, ∞)
Odd/Even: Even
Period: 2𝜋𝜋
=
=
1
sin(𝑥𝑥)
1
cos(𝑥𝑥)
𝑓𝑓(𝑥𝑥) = cot(𝑥𝑥)
Cotangent
Graph of Function
=
=
1
tan(𝑥𝑥)
cos(𝑥𝑥)
sin(𝑥𝑥)
General Form: 𝑓𝑓(𝑥𝑥) = 𝑎𝑎 sin[𝑏𝑏(𝑥𝑥 − ℎ)] + 𝑘𝑘
Mohawk Valley Community College
Domain: (−∞, ∞) except for
𝑥𝑥 = ±𝑛𝑛𝑛𝑛
Range: (−∞, ∞)
Odd/Even: Odd
Period: 𝜋𝜋
Asymptotes at 𝑥𝑥 = ±𝑛𝑛𝑛𝑛
*This general form can be used for any trigonometric function*
Learning Commons Math Lab IT129
Graphs of Inverse Trigonometry Functions
Function
Name
Parent
Function
Inverse Sine
𝑓𝑓(𝑥𝑥) = sin−1 (𝑥𝑥)
Inverse
Cosine
𝑓𝑓(𝑥𝑥) = cos−1(𝑥𝑥)
Inverse
Tangent
𝑓𝑓(𝑥𝑥) = tan−1 (𝑥𝑥)
Inverse
Cosecant
𝑓𝑓(𝑥𝑥) = csc −1 (𝑥𝑥)
Inverse
Secant
𝑓𝑓(𝑥𝑥) = sec −1 (𝑥𝑥)
Inverse
Cotangent
𝑓𝑓(𝑥𝑥) = cot −1 (𝑥𝑥)
= arcsin(𝑥𝑥)
= arccos(𝑥𝑥)
= arctan(𝑥𝑥)
= arccsc(𝑥𝑥)
= arcsec(𝑥𝑥)
= arccot(𝑥𝑥)
Mohawk Valley Community College
Graph of Function
Characteristics
Domain: [−1,1]
Range: �
−𝜋𝜋 𝜋𝜋
, �
2 2
Domain: [−1,1]
Range: [0, 𝜋𝜋]
Domain: (−∞, ∞)
−𝜋𝜋 𝜋𝜋
, �
2 2
Range: �
Domain: (−∞, −1] ∪ [1, ∞)
Range: �
−𝜋𝜋 𝜋𝜋
, � , 𝑦𝑦
2 2
≠0
Domain: (−∞, −1] ∪ [1, ∞)
Range: [0, 𝜋𝜋], 𝑦𝑦 ≠
𝜋𝜋
2
Domain: (−∞, ∞)
Range: (0, 𝜋𝜋)
Learning Commons Math Lab IT129