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Sin Formula
The sine function, often known as the sin function, is indeed a periodic function in trigonometry. In a right-angled triangle, a sine function can be defined as the ratio of a length of a perpendicular towards the length of the hypotenuse.
Sin Formula Definition
The ratio of the perpendicular (opposite to an angle) to a hypotenuse is the sin of an angle in a right-angled triangle. This sin formula is written as follows:
Sinθ = Perpendicular/Hypotenuse
Sinθ + 2nπ = Sinθ for all θ
Sin(-θ) = -Sinθ
Sin Table
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 |
Solved Examples
Example 1: Find the value of sin(780)º.
Solution:
sine(780º) = sine(720º + 60º)
sine(780º) = sine(60º)
Sin(780)º = Sin(60)º = √3/2
Hence the value of Sin(780º) = √3/2 (Answer)
Example 2: Find the value of Sin(420)º
Solution:
420º = 360º + 60º
420º = 60º
Sin(420)º = Sin(60)º = √3/2
Hence, Sin(420)º = √3/2 (Answer)
