Sin Formula
Before going to learn the sin formula, let us recall a few things about the sin function. In trigonometry, the sine function or sin function is a periodic function. The sine function can also be defined as the ratio of the length of the perpendicular to that of the length of the hypotenuse in a rightangled triangle. Sin is a periodic function with a period of 2π, and the domain of the function is (−∞, ∞) and the range is [−1,1]. Sin formula is used to find sides of a triangle.
What Is the Sin Formula?
The sine of an angle of a rightangled triangle is the ratio of its perpendicular (that is opposite to the angle) to the hypotenuse. The sin formula is given as:
 sin θ = Perpendicular / Hypotenuse.
 sin(θ + 2nπ) = sin θ for every θ
 sin(−θ) = − sin θ
Sin value table is given below:
Sine Degrees  Sine Values 
Sine 0°  0 
Sine 30°  1/2 
Sine 45°  1/√2 
Sine 60°  √3/2 
Sine 90°  1 
Sine 120°  √3/2 
Sine 150°  1/2 
Sine 180°  0 
Sine 270°  1 
Sine 360°  0 
Let us see the applications of the sin formula in the following section.

Example 1: Find the value of sin780^{o}.
Solution
To find: The value of sin 780^{o }using the sin formula.
We have:
780^{o }= 720^{o }+ 60^{o}
⇒780^{o }= 60^{o}
⇒sin(780^{o}) = sin(60^{o}) = √3/2
Answer: The value of sin780^{o} is √3/2.

Example 2: Find the length of perpendicular for the given triangle if the length of a hypotenuse is 5, and it is known that sinθ = 0.6.
Solution:
To find: The length of perpendicular
Given, sinθ = 0.6
Using the sin formula,
sinθ = Perpendicular / Hypotenuse
⟹0.6 = Perpendicular / Hypotenuse
⟹0.6 = x / 5
⟹x = 3
Answer: The length of the perpendicular is 3 units.
Steps to find the volume of a pyramid:
Step 1: Find the area of the base
Step 2: Multiply the area by the height of the pyramid
Step 3: Divide by 3