Hamza

January 26, 2021

Chapters

Sine Function
y = sin x
Cosine Function
y = cos x
Tangent Function
y = tan x
Cotangent Function
y = cot x
Secant Function
y = sec x
Cosecant Function
y = csc x

Sine Function

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y = sin x

Domain: $\mathbb{R}$

Range: $[-1, 1]$

Period: $2 \pi rad$

Continuity: Continuous in $\forall x \in \mathbb{R}$

Odd function: $\sin { (-x) } = -\sin { (x) }$

Cosine Function

y = cos x

Domain: $\mathbb{R}$

Range: $[-1, 1]$

Period: $2 \pi rad$

Continuity: Continuous in $\forall x \in \mathbb{R}$

Even function: $\cos { (-x) } = \cos { (x) }$

Tangent Function

y = tan x

Domain: $\mathbb{R} - \left \{ (2k + 1) . \frac { \pi }{ 2 }, k \in \mathbb{Z} \right \} = \mathbb{R} - \left \{ ... , - \frac { \pi }{ 2 }, \frac { \pi }{ 2 }, \frac { 3 \pi }{ 2 }, ... \right \}$

Range: $\mathbb{R}$

Continuity: Continuous in $\forall x \in \mathbb{R} - \left \{ ( \frac { \pi }{ 2 } + \pi . k) \right \}$

Period: $\pi rad$

Odd function: $\tan { (- x) } = - \tan { (x) }$

Cotangent Function

y = cot x

Domain: $\mathbb{R} - \left \{ k . \pi, k \in \mathbb{Z} \right \} = \mathbb{R} - \left \{ ... , - \pi, 0, \pi, ... \right \}$

Range: $\mathbb{R}$

Continuity: Continuous in $x \in \mathbb{R} - \left \{ \pi . k , k \in \mathbb{Z} \right \}$

Period: $\pi rad$

Odd function: $\cot { (-x) } = - \cot { ( x ) }$

Secant Function

y = sec x

Domain: $\mathbb{R} - \left \{ (2k + 1) . \frac { \pi }{ 2 }, k \in \mathbb{Z} \right \} = \mathbb{R} - \left \{ ..., - \frac { \pi }{ 2 }, \frac { \pi }{ 2 }, \frac { 3 \pi }{ 2 }, ... \right \}$

Range: $(- \infty , -1] \cup [1, \infty )$

Period: $2 \pi rad$

Continuity: Continuous in $\forall x \in \mathbb{R} - \left \{ ( \frac { \pi }{ 2 } + \pi . k) \right \}$

Even function: $\sec { (-x) } = \sec { (x) }$

Cosecant Function

y = csc x

Domain: $\mathbb{R} \left \{ k . \pi, k \in \mathbb{Z}\right \} = \mathbb{R} - \left \{ ..., - \pi, 0, \pi, ... \right \}$

Range: $( - \infty, -1] \cup [1, \infty)$

Period: $2 \pi rad$

Continuity: Continuous in $x \in \mathbb{R} - \left \{ \pi . k, k \in \mathbb{Z} \right \}$

Odd function: $\cosec { (-x) } = - \cosec { x }$

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Hamza

Hi! I am Hamza and I am from Pakistan. My hobbies are reading, writing and playing chess. Currently, I am a student enrolled in the Chemical Engineering Bachelor program.

Trigonometric Functions

Sine Function

y = sin x

Cosine Function

y = cos x

Tangent Function

y = tan x

Cotangent Function

y = cot x

Secant Function

y = sec x

Cosecant Function

y = csc x

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Theory

Exponent Rules

Absolute Value Function

Asymptotes

Bounded Functions

Bounded Sequence

Composition of Functions

Constant Functions

Convergent and Divergent Sequences

Coordinates in the Plane

Even and Odd Functions

Exponential Function

Graphing polynomial function I

Graphing logarithmic function

Graphing polynomial function II

Graphing rational function II

Graphing rational function IV

Graphing rational function V

Graphing rational function 8

Graphing exponential function I

Geometric Sequence

Graphing Functions

x- and y-Intercepts

Inverse Function

L’Hôpital’s Rule

Limit of a Sequence

Logarithmic Functions

Absolute and Relative Maxima and Minima

Maxima and Minima

nth Term

Optimization

Properties of Limits

Quadratic Function

Rational Functions

Sequences

Types of Functions

Graphing Parabolas

Arithmetic Sequence

Mean Value Theorem

Rolle’s Theorem

Intervals of Increase and Decrease

Periodic Functions

Concave and Convex Functions

Graphing rational function I

Graphing rational function III

Inflection Points

Increasing and Decreasing Functions

Geometric Sequence Problems

Piecewise Functions

Arithmetic Sequence Problems

Linear Function

Domain of a Function

Maxima, Minima and Inflection Points

Graphing exponential function II

Linear Functions Worksheet

Monotone Sequence

Radical Functions

Function

Formulas

Sequence Formulas

Exercises

Absolute Value Functions Worksheet

Asymptotes Worksheet

Even and Odd Functions Worksheet

Inflection Points Worksheet

X- and Y-Intercepts Worksheet