What is sin 120 degrees ?

To find the sine of 120 degrees, we can use our understanding of the unit circle and the properties of trigonometric functions. The sine function is related to the y-coordinate of a point on the unit circle, which is a circle with a radius of 1 centered at the origin of a coordinate plane.

Locating 120 Degrees on the Unit Circle

First, let's visualize where 120 degrees lies. The unit circle is divided into four quadrants:

• Quadrant I: 0 to 90 degrees
• Quadrant II: 90 to 180 degrees
• Quadrant III: 180 to 270 degrees
• Quadrant IV: 270 to 360 degrees

Since 120 degrees is between 90 and 180 degrees, it is located in the second quadrant. In this quadrant, the sine values are positive.

Reference Angle

To find the sine of 120 degrees, we can also use the concept of a reference angle. The reference angle for any angle in the second quadrant can be found by subtracting it from 180 degrees:

Reference angle = 180 degrees - 120 degrees = 60 degrees

This means that the sine of 120 degrees is the same as the sine of its reference angle, 60 degrees.

Calculating Sine of 60 Degrees

Now, we need to recall the sine value for 60 degrees. From trigonometric values, we know:

sin(60 degrees) = √3/2

Since 120 degrees is in the second quadrant where sine is positive, we have:

sin(120 degrees) = sin(60 degrees) = √3/2

Final Result

Thus, the sine of 120 degrees is:

sin(120 degrees) = √3/2

This value can be useful in various applications, such as solving triangles or in physics problems involving angles. Understanding how to find sine values using the unit circle and reference angles is a fundamental skill in trigonometry.