Sine

A mathematical relation between angle and ratio of lengths of opposite side to hypotenuse of a right angled triangle is called sine.

Mathematical form

right angled triangle

$\Delta BAC$ is a right angled triangle.

$(1) \,\,\,\,\,\,$ $BC$ is length of the opposite side.
$(2) \,\,\,\,\,\,$ $AC$ is length of the hypotenuse.
$(3) \,\,\,\,\,\,$ Theta ($\theta$) is angle of the triangle $BAC$

In trigonometry, sine is written as $\sin$ to express it mathematically in short form but it depends on the angle and ratio of lengths of opposite side to hypotenuse.

Thus, sine is usually written along with angle and made it equal to ratio of lengths of opposite side to hypotenuse for expressing the relation between them in the form of sine meaningfully.

$\sin{\theta} \,=\, \dfrac{BC}{AC}$

$\sin{\theta}$ is read as sine of angle theta. Sine is defined in trigonometry on the basis of ratio of lengths of two sides. Hence, it is called as a trigonometric ratio. Similarly, it works on a mathematical relation between angle and ratio of lengths opposite side to hypotenuse. Therefore, it is generally called as sine function.



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