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Trigonometry
Trigonometry1
Trigonometry
The word Trigonometry is originated from the Greek word ‘Tri’ which means three, ‘gonia’ means angle and metron means measure, i.e. it is the study of geometrical figures which have three angles. Trigonometry helps us find angles and distances. It is all about triangles…..
The most interesting triangle is RIGHT ANGLED TRIANGLE
We can define 6 possible ratios among the three sides of the triangle AOB, known as trigonometric ratios, they are defined as follows:
Pythagorean triplets
Pythagorean triplets consists of 3 positive numbers a, b, c which satisfies Pythagoras theorem a^{2}=b^{2}+c^{2}
Some examples are as follows:
(3, 4, 5)
(6, 8, 10)
(5, 12, 13)
(7, 24, 25)
(8, 15, 17)
(9, 40, 41)
The Pythagorean triplets describe the 3 integer side lengths of right angle triangle. However, right triangles with noninteger sides do not form Pythagorean triples. E.g., a = b = 1 so c =√2, But (1, 1,√2) is not a Pythagorean triplet.
Trigonometric angles
Learn how to calculate base and perpendicular of a right angled triangle
Pythagorean identities
1) sin^{2}θ+ cos^{2}θ=1
2) 1+tan^{2}θ= sec^{2}θ
3) 1+ cot^{2}θ=cosec^{2}θ
Odd Even identities
sin (θ) = sinθ
cos (θ) = cosθ
tan (θ) = tanθ
cot (θ) = cotθ
(θ) = cosecθ
sec (θ) = secθ
ASTC rule aka also Sin Tan Cos rule
* NOTE: The ASTC rule is to be read in clock wise direction, this means (90 +) will lie in 2nd quadrant
‘Sine’ will change to ‘cos’ and ‘tan’ will change to ‘cot’ and ‘cos’ will change to ‘sec’ and vice versa when angle is in the form 90K±θ where k is odd, otherwise there will be no changes.

When lies in the first quadrant then all trigonometric ratios are positive.
2) When lies in the second quadrant then sine and cosecant are positive other trigonometric ratios sin, cosec, tan and cot are negative.
3) When lies in the third quadrant then tangent and cotangent are positive other trigonometric ratios sin, cosec, tan and cot are negative.
4) When lies in the fourth quadrant then cosine and secant are positive other trigonometric ratios sin, cosec, tan and cot are negative.
Other formulae
sin a+b =sin a cos b +cos asin b
sin ab =sinacos bcos asin b
cos (a+b) =cos acos bsin asin b
cos ab =cos acos b+sin asin b