**2 Dimensional Shapes – Geometry** is the study of shapes and size. The structures are called **2-Dimensional shapes** if they consist of only two dimensions and can be represented in x-y coordinate axis! The general dimensions for any 2-D geometric structure are the length and the width in the x and y direction.

### Month: September 2017

# What is Vectors in Math

**Vectors:** Any quantity can be described in 2 ways: a **Scalar** or **Vector**. **‘Scalar’** is a quantity which only has magnitude (number only). ‘**Vector’** is a quantity which has both magnitude and direction (which way it’s heading towards).

# Foundation for functions – Algebra Lesson (Mathematics )

# What is a Function?

A function can be expressed in many ways, some of them being linear, quadratic, logarithmic functions etc. But just like numbers there are operations which can be used even on functions.

**Addition and Subtraction between functions:**

# How To Write The Best College Assignment? Follow the General Advice

Intelligent students can effortlessly write a best college assignments. Professors and teachers are conscious of the actual fact that many students aren’t able to write properly because they fall short of their skills or passion to write effectively. Numerous subjects are taught in the universities. At times few learners aren’t keen to write their college assignment. But they cannot overlook its significance as they won’t do anything good to themselves. As a learner, if you don’t know how to write assignments appropriately, then you can take a help!

# What is Expressions, Equations and Relationships ?

**Expression** is a simple math relationship between a variable and a number. The **variable **is the quantity which can take any value accordingly (usually represented by an **alphabet**). However an **Equation** relates two different expressions with an **‘equality’** sign

**Examples of Expressions:**

# What is Convergence and Divergence in Calculus Mathematics ?

**Convergence and Divergence –** In **Sequences and Series**, we can find whether the given function converges or diverges. **A function is said to converge if its limit value exists and is finite**. **A function is said to diverge if it’s limit value does not exist(or rather approaches infinity).**

# Congruence and geometry of size

**Congruence geometry:** If two objects are of same exact shape and same exact size, then they are called **congruent objects**. The congruent objects are more like duplicates of each other and fit perfectly when placed on top of each other.

In geometry, congruency is an important property and whenever two geometric shapes have same shape and length, then the angles of one shape are also equal to the other.

**Example:**

The symbol used to denote congruency is, ‘≡’ which means that the structures are of same shape and equal size.

**Congruency in triangles:**

**Theorems:**

**SSS: **3 sides of one triangle=3 sides of the other

**2) SAS :2** sides and included angle of one triangle=2 sides and included angle of other.

**3)ASA :**2 angles and included side one triangle= 2 angles and included side of other.

**4) AAS :**2angles and non-included side=2angles and non-included side of other

**Example: **If ∆ ABC≡∆DEF and BC=10 units, then EF=? EF=10 (since BC=EF )

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You can also Read our other blog Angle Definition And Properties (Trigonometry) |

# Angle definition and properties (Trigonometry)

**Angle Definition : Angle** is the **measure of rotation** formed between two rays. In trigonometry, angles play a huge role in determining the appropriate trigonometric function values. **One complete rotation gives an angle of** **360°**. Depending on the direction of rotation, angles can be positive or negative!

**Units of Angle: **Angle is either measured in **degrees **or in **radians.**

**Radian: **It is the standard unit to measure an angle and is numerically equal to the length of its respective arc of a unit circle.

**Conversion of degree to radian: **There is a simple relationship between degrees and radians.

** Π radians = 180°**

So **1radian=180°/Π** (OR) **1degree=π/180°**

**Example: **Convert 120° to radian.

120°* (π /180°) = **2π/3 radian**

**Example: **Convert π/6 radian to degrees.

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You can also Read our other blog Intro To Inverse Trigonometric Functions |

# How do Find that equation is a linear or nonlinear function?

How to find Linear or Nonlinear Function. **Linear functions** are of the general form, f(x) = ax+b, where ‘a’ and ‘b’ are constants. The relationship between ‘x’ and ‘f(x)’ in a linear equation gives us a straight line and the constants ‘a’ and ‘b’ gives us additional details about how the straight line is formed.

This relationship can be expressed either in algebraic form like an equation, or in graphical form by drawing graphs.

General ordered pair** -> **

Function notation **-> **

**Example:** Given are two coordinate points in function notation, write down in ordered pairs form.

f(3) = 10 f(0) = -4 f(-6) = 17

(x, y) = (3,10) (x,y) = (0,-4) (x,y) = (-6,17)

**Example: **If f(x) = 2x + 3, find f(0), f(1), f(-1).

Answer: This might look tricky, but simply follow the steps!

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You can also Read our other blog What Is Linear Equation And Inequalities ? |

# Intro to inverse Trigonometric functions

### inverse Trigonometric functions

In trigonometry, if an angle is given then using any of the 6 trigonometric functions we find its trigonometric function value. But if the trigonometric function value is given, then finding the angle (working backwards) using a function is called Inverse trigonometric function.