What is Trigonometry?

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What is Trigonometry?

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.




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How Sin(2A) = 2SinA CosA or Sin(A) = 2Sin(A/2) Cos(A/2) ?

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Derivation of   Sin(2A) = 2 SinA CosA or Sin(A) = 2Sin(A/2) Cos(A/2)? As we know that, ⇒Sin(A+B) = SinA CosB + CosA SinB 👉👉( Sin(A+B) = SinA CosB + CosA SinB ) put B= A then, ⇒Sin(A+A) = SinA CosA + CosA SinA    ⇒Sin(2A) = SinA CosA + SinA CosA Hence, Sin(2A) = 2SinA CosA ⇒If angle will be halfed i.e. θ = A ⇒Hence,        Sin(A) = 2Sin(A/2) Cos(A/2)
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How Sin²Î¸ + Cos²Î¸ = 1?

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How   Sin²Î¸ + Cos²Î¸ = 1...?? According to Pythagoras theorem, "the square of hypotenuse(H) is equal to the sum of square of base(B) and perpendicular(P)" i.e.     H² = B² + P² (Dividing both sides by H²) we get,     H²/H² = B²/H² + P²/H²        1   = Sin²Î¸ + Cos²Î¸                       ....(B/H  = sinθ and P/H = cosθ) Hence, Sin²Î¸ + Cos²Î¸ = 1 How Sin²Î¸ + Cos²Î¸ = 1?
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Trigonometric values w.r.t. Quadrants (1st, 2nd, 3rd and 4th)

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👉Important Rules for trigonometric values in 1st ,2nd ,3rd and 4th Quadrant. {1}.    Quadrant 1st: (90°-θ) and (360°+θ) All Trigonometric values are Positive (+). {2}. Quadrant 2nd :  (90°+θ) and (180°-θ) Only values of sine (sin) and Cosecant (cosec) is positive (+) rest all Trigonometric values are negative (-). {3}. Quadrant 3rd:  (180°+θ) and (270°-θ) Only values of tangent (tan) and Cotangent (cot) is positive (+) rest all Trigonometric values are negative (-). {4} . Quadrant 4th :  (270°+θ) and (360° -θ) Only values of cosine (cos) and Secant (sec) is positive (+) rest all Trigonometric values are negative (-). 👇 The picture showing the values of all Trigonometric ratios in different quadrants :- # A Simple Way to remember A DD : All values positive S UGAR : Sine,Cosine are positive T O : Tan, cot are positive C OFEE : cos ,sec are positive
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