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.
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).
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:
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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:
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 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 : 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 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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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.