The formula for finding the sine of an angle is sin(x) = opposite/hypotenuse, where x is the given angle.
To find the value of sin 120 degrees, you can use a scientific calculator or a trigonometric table. Alternatively, you can use the half-angle formula for sine (sin(x/2) = ±√[(1-cosx)/2]) to simplify the calculation.
Yes, you can find the sine of 120 degrees without a calculator by using the half-angle formula or by using the unit circle and knowing the trigonometric values for common angles (such as 30, 45, and 60 degrees).
The sine of 120 degrees is negative because it falls in the second quadrant of the unit circle, where the sine values are negative. This means that the opposite side of the triangle is below the horizontal axis, resulting in a negative ratio (opposite/hypotenuse).
Knowing the sine of 120 degrees can be useful in various fields such as engineering, physics, and astronomy. For example, it can be used to calculate the height of a building or the trajectory of a projectile. It can also be used to determine the angular velocity of a rotating object.
