How to Find Sine of any Angle?

Last Updated : 02 Mar, 2024

In a right-angled triangle ABC, where angle A is the angle of interest, and side lengths are denoted as follows:

• Opposite side (opposite to angle A): a
• Adjacent side (next to angle A): b
• Hypotenuse (opposite the right angle): c

The sine of angle A (sin A) is calculated as: sin A = [Tex]\bold{\frac{a}{c}}[/Tex].

Therefore, to find the sine of any angle A in a right-angled triangle, you can use the formula:

sin A = [Tex]\bold{\frac{length of the opposite side}{length of the hypotenuse}}[/Tex]

Sine of any angle

The sine of any angle in a right-angled triangle can be found using the following formula:

[Tex] \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}[/Tex]

Sine of some common angles

For common angles like 30Â°, 45Â°, 60Â°and 90Â°, exact values of sine are known:

[Tex]\bold{\sin(30^\circ) = \frac{1}{2} }[/Tex]â€‹

[Tex]\bold{\sin(45^\circ) = \frac{\sqrt{2}}{2}}[/Tex]

[Tex]\bold{\sin(60^\circ) = \frac{\sqrt{3}}{2}}[/Tex]

[Tex]\bold{\sin(90^\circ) = 1 }[/Tex]