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.
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.
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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.
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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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