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Mathematics, computing assignment
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Basic knowledge Natural numbers: numbers starting from
1 are natural numbers. 1,2,3,4,………………
Whole numbers: numbers starting from 0 are whole numbers. 0,1,2,3,4,…………………….
Integers: whole numbers + negative numbers are integers. …………..,-2,-1,0,1,2,……………
Rational numbers: numbers that can be expressed in the form of p/q where q≠0
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Sets
Sets is a well defined collection of objects.
SUBSETS: a Set A is said to be subset of a set B if every element of A is also an element of B.
BA
A=B
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OPERATIONS ON SETS
UNION: The union of A and B is the set which consist of all the elements of A and B
AUB
A u B= A +B- A intersection B
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INTERSECTION: It is the set of all the elements which are common to both A and B
NO INTERSECTION
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TRIGONOMETRIC FUNCTIONS
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Sin function
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Cos function
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Tan function
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Cot function
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Cosec function
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Sec function
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Basic and Pythagorean Identities
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1.sin2(t) + cos2(t) = 1 2. tan2(t) + 1 = sec2(t) 3. 1 + cot2(t) = csc2(t)
1. sin(–t) = –sin(t) 2.cos(–t) = cos(t) 3.tan(–t) = –tan(t)
identities
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Angle-Sum and -Difference Identities
sin(α + β) = sin(α)cos(β) + cos(α)sin(β) sin(α – β) = sin(α)cos(β) – cos(α)sin(β) cos(α + β) = cos(α)cos(β) – sin(α)sin(β) cos(α – β) = cos(α)cos(β) + sin(α)sin(β)
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Double-Angle Identities
sin(2x) = 2sin(x)cos(x) cos(2x) = cos2(x) – sin2(x) = 1 – 2sin2(x) = 2cos2(x) – 1
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Sum Identities
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Product Identities
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Geometry
circle: it is set of all points that are equidistant from a fixed point in the plane.
centre
equation:(x-j)2 + (y-k)2 = r2
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Parabola: a parabola is the set of all points in a plane that are equidistant from a fixed line and a fixed point in the plane.
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ellipse
It is the set al all the points in a plane, the sum of whose distance from two fixed points in the plane is constant.
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