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From when I saw <math> cin\theta </math> I knew the rest of the comic would be <math> \frac{b}{s}</math>.  [[User:Observer of the Absurd|Observer of the Absurd]] ([[User talk:Observer of the Absurd|talk]]) 13:28, 15 May 2019 (UTC)
 
From when I saw <math> cin\theta </math> I knew the rest of the comic would be <math> \frac{b}{s}</math>.  [[User:Observer of the Absurd|Observer of the Absurd]] ([[User talk:Observer of the Absurd|talk]]) 13:28, 15 May 2019 (UTC)
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== List of Essential Trigonometry formulas for Class 10, 11, and 12 ==
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Trigonometry formulas (source:https://inspiria.edu.in/trigonometry-formulas-for-class-12/)
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If you are looking for the complete list of all trigonometry formulas for classes 10, 11, and 12, we have made it completely easy for you to understand and learn all trigonometry formulas and ratios to a single page. Memorizing these trigonometric formulas help students to solve trigonometry problems easily, which further leads to a good score in Mathematics. For easy understanding and access, we have provided the trigonometry table and inverse trigonometry formulas.
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Trigonometry, a word derived from the Greek words ‘Trigon’ and ‘Metron’ refers to ‘measuring the sides of a triangle. This branch of mathematics studies the relation between angles and sides of triangles. Trigonometry formulas are  used widely in various fields and have been in use since the 3rd Century BC. From Navigation to Celestial Mechanics to Engineering, Architecture and other various fields trigonometry play a vital role.
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Various geometrical problems are solved using the trigonometry ratios Sine (Sin), Cosine (Cos), Tangent (Tan), Cotangent (cot), Secant (sec), and Cosecant (Csc), product identities, Pythagorean Identities, etc. There are several Trigonometric functions, formulas, and ratios like the sign of ratios in different quadrants, sum identities, difference identities, cofunction identities, double angle identities, half-angle identities, etc.  These are introduced from Class 10th and the concept is further explained in classes 11th & 12th.
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Trigonometry Formulas for Class 10, 11, and 12:
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As trigonometry is the study of relationships between angles and sides of the triangles. The primary triangle studied is the right triangle. In a right-angled triangle, the three sides are named Hypotenuse, Opposite, and Adjacent. The longest side is called the Hypotenuse, the opposite side to the angle is called the Perpendicular (Opposite), and the side where both hypotenuse and opposite sits is the adjacent side.
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Basic Formulas
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Reciprocal Identities
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Trigonometry Table
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Periodic Identities
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Co-function Identities
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Sum and Difference Identities
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Double Angle Identities
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Triple Angle Identities
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Half Angle Identities
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Product Identities
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Sum to Product Identities
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Inverse Trigonometry Formulas
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Basic Formulae
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The basic Trigonometry formulas for class 10 are six basic ratios which are used for finding the elements in trigonometry which are called trigonometric functions. These are Sine (Sin), Cosine (Cos), Tangent (Tan), Cotangent (Cot), Secant (Sec), and Cosecant (Csc).
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By taking right triangle as a reference, these Trigonometry functions are derived as following:
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sin θ = Opposite Side/Hypotenuse
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cos θ = Adjacent Side/Hypotenuse
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tan θ = Opposite Side/Adjacent Side
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sec θ = Hypotenuse/Adjacent Side
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cosec θ = Hypotenuse/Opposite Side
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cot θ = Adjacent Side/Opposite Side
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Reciprocal Identities
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Reciprocal identities are given as following:
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cosec θ = 1/sin θ
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sec θ = 1/cos θ
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cot θ = 1/tan θ
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sin θ = 1/cosec θ
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cos θ = 1/sec θ
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tan θ = 1/cot θ
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These are taken from a right-angled triangle. As the height and base of the right triangle are given, we can find out the Sine (sin), Cosine (cos), Tangent (tan), Cotangent (cot), Secant (sec), and Cosecant (CSC) values using trigonometric formulas. These reciprocal trigonometric identities can also be derived by using the trigonometric functions.
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Trigonometry Table
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Below is the table for trigonometry formulas for angles that are commonly used for solving problems.
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Angles (In Degrees)
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30°
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45°
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60°
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90°
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180°
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270°
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360°
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Angles (In Radians)
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π/6
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π/4
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π/3
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π/2
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π
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3π/2
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sin
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0
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1/2
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1/√2
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√3/2
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1
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0
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-1
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0
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cos
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1
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√3/2
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1/√2
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1/2
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0
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-1
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0
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1
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tan
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0
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1/√3
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1
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√3
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0
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0
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cot
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√3
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1
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1/√3
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0
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0
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csc
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2
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√2
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2/√3
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1
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-1
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sec
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1
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2/√3
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√2
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2
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-1
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1
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Periodicity Identities in Radian
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After the basic formulas Trigonometry formula for Class 11 introduces periodicity Identities used in shifting the trigonometric functions by one period to the left or right. These are called co-function identities.
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sin (π/2 – A) = cos A & cos (π/2 – A) = sin A
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sin (π/2 + A) = cos A & cos (π/2 + A) = – sin A
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sin (3π/2 – A)  = – cos A & cos (3π/2 – A)  = – sin A
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sin (3π/2 + A) = – cos A & cos (3π/2 + A) = sin A
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sin (π – A) = sin A &  cos (π – A) = – cos A
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sin (π + A) = – sin A & cos (π + A) = – cos A
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sin (2π – A) = – sin A & cos (2π – A) = cos A
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sin (2π + A) = sin A & cos (2π + A) = cos A
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We know tall trigonometry functions in Class 11 are repetitive in nature, repeating themselves after this periodicity constant. This periodicity constant is different for different trigonometric identities. tan 45° = tan 225° but this is also true for cos 45° and cos 225°.
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Co-function Identities (in Degrees
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The co-function or periodic identities can also be represented in degrees as:
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sin(90°−x) = cos x
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cos(90°−x) = sin x
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tan(90°−x) = cot x
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cot(90°−x) = tan x
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sec(90°−x) = csc x
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csc(90°−x) = sec x
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Sum & Difference Identities
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sin(x+y) = sin(x)cos(y)+cos(x)sin(y)
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cos(x+y) = cos(x)cos(y)–sin(x)sin(y)
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tan(x+y) = (tan x + tan y)/ (1−tan x •tan y)
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sin(x–y) = sin(x)cos(y)–cos(x)sin(y)
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cos(x–y) = cos(x)cos(y) + sin(x)sin(y)
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tan(x−y) = (tan x–tan y)/ (1+tan x • tan y)
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Double Angle Identities
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sin(2x) = 2sin(x) • cos(x) = [2tan x/(1+tan2 x)]
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cos(2x) = cos2(x)–sin2(x) = [(1-tan2 x)/(1+tan2 x)]
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cos(2x) = 2cos2(x)−1 = 1–2sin2(x)
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tan(2x) = [2tan(x)]/ [1−tan2(x)]
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sec (2x) = sec2 x/(2-sec2 x)
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csc (2x) = (sec x. csc x)/2
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Triple Angle Identities
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Sin 3x = 3sin x – 4sin3x
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Cos 3x = 4cos3x-3cos x
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Tan 3x = [3tanx-tan3x]/[1-3tan2x]

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