{"id":259309,"date":"2024-07-03T14:01:03","date_gmt":"2024-07-03T14:01:03","guid":{"rendered":"https:\/\/namso-gen.co\/blog\/?p=259309"},"modified":"2024-07-03T14:01:03","modified_gmt":"2024-07-03T14:01:03","slug":"what-is-the-value-of-sin-120","status":"publish","type":"post","link":"https:\/\/namso-gen.co\/blog\/what-is-the-value-of-sin-120\/","title":{"rendered":"What is the value of sin 120?"},"content":{"rendered":"

What is the value of sin 120?
\nThe value of sin 120 degrees is \u221a3\/2.<\/p>\n

Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. One of the most commonly used trigonometric functions is sine, denoted as sin. The sine of an angle in a right-angled triangle is defined as the ratio of the length of the side opposite the angle to the hypotenuse.<\/p>\n

The question arises, what is the value of sin 120? To find the answer, we need to understand the concept of the unit circle. The unit circle is a circle with a radius of 1 unit, centered at the origin of a coordinate system.<\/p>\n

When an angle is measured in degrees, as in this case, the positive x-axis is considered as 0 degrees, and angles are measured counterclockwise. So, if this unit circle is divided into 360 degrees, we can find the value of sin 120 by determining the y-coordinate of the point on the unit circle that corresponds to 120 degrees.<\/p>\n

To calculate sin 120, we draw a line from the origin to the point P on the unit circle that forms a 120-degree angle with the positive x-axis. This line segment divides the unit circle into two equal parts. The y-coordinate of point P represents the sine value for the angle 120 degrees.<\/p>\n

Now, let’s find the value of sin 120. By observing the unit circle, we can see that point P lies in the second quadrant. The y-coordinate in this quadrant is positive, and the x-coordinate is negative. To determine the length of the y-coordinate, we calculate the perpendicular distance from point P to the x-axis.<\/p>\n

Since the unit circle has a radius of 1 unit, the perpendicular distance from point P to the x-axis is equal to the altitude of an equilateral triangle with a side length of 1 unit. By using the Pythagorean theorem, we can find this altitude as follows:<\/p>\n

(Side length)^2 = (Altitude)^2 + (1\/2 * Side length)^2
\n 1^2 = (Altitude)^2 + (1\/2)^2
\n (Altitude)^2 = 1 – 1\/4
\n (Altitude)^2 = 3\/4
\n Altitude = \u221a3\/2<\/p>\n

Therefore, the y-coordinate, which is equal to the value of sin 120, is \u221a3\/2. **The value of sin 120 is \u221a3\/2.** It signifies that the sine of 120 degrees is positive and equal to \u221a3\/2.<\/p>\n

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