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 30°, 45°, 60°and 90°, exact values of sine are known:
[Tex]\bold{\sin(30^\circ) = \frac{1}{2} }[/Tex]​
[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]
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