Sin Theta Formula
In a Right-angled triangle, the sine function or sine theta is defined as the ratio of the opposite side to the hypotenuse of the triangle. In a triangle, the Sine rule helps to relate the sides and angles of the triangle with its circumradius(R) i.e, a/SinA = b/SinB = c/SinC = 2R. Where a, b, and c are lengths of the triangle, and A, B, C are angles, and R is circumradius.
Sin θ = (Opposite Side / Hypotenuse)
From the above figure, sine θ can be written as
sin θ = AB / AC
According to the Pythagoras Theorem,
We know that AB2 + BC2 = AC2
Dividing both sides by AC2
⇒ (AB/AC)2 + (BC/AC)2 = (AC/AC)2
⇒ Sin2θ + Cos2θ = 1
Formula of Sin Theta
Various formulas related to sin θ are,
- Sin (- θ) = – sin θ
- Sin (90 – θ) = cos θ
- Sin (180 – θ) = sin θ
- sin2 θ + cos2 θ = 1
- sin (A+B) = Sin A×Cos B + Cos A×Sin B
- sin (A-B) = Sin A×Cos B – Cos A×Sin B
- Sin 2 θ = 2 sin θ. cos θ
- Sin 3 θ = 3 sin θ – 4 sin3 θ
Sin Theta Formula
Trigonometry, a branch of mathematics, is a powerful tool that helps us understand the relationships between the angles and sides of triangles. One of the fundamental concepts in trigonometry is the sine function, often represented as sin(θ), where θ is an angle.
This article will delve into the sin theta formula and its applications.
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