Sin Formula - Learn The Formula To Calculate Sin Values - Cuemath

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 right-angled 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.

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What Is the Sin Formula?

The sine of an angle of a right-angled 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.

Solved Examples Using Sin Formula

1. Example 1: Find the value of sin780o.

   Solution

   To find: The value of sin 780o using the sin formula.

   We have:

   780o = 720o + 60o

   ⇒780o = 60o

   ⇒sin(780o) = sin(60o) = √3/2

   Answer: The value of sin780o is √3/2.

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

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