How to Calculate sin(120°) | Understanding the Sine Function and Using the Unit Circle

sin(120°)

To calculate the value of sin(120°), we first need to understand the concept of the sine function

To calculate the value of sin(120°), we first need to understand the concept of the sine function. In trigonometry, the sine of an angle within a right triangle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.

In this case, we are dealing with an angle of 120 degrees. However, we have to keep in mind that the sine function is typically defined for acute angles (less than 90 degrees) within a right triangle.

To solve this, we can use the concept of the unit circle. The unit circle is a circle with a radius of 1 unit centered at the origin in a coordinate plane. Any point on the unit circle corresponds to an angle measured from the positive x-axis in a counterclockwise direction.

In the case of 120 degrees, we can locate the corresponding angle on the unit circle by drawing a line from the origin in the counterclockwise direction. This line will intersect the unit circle at a specific point.

For 120 degrees, we find that the corresponding point on the unit circle is at coordinates (-0.5, √3/2).

Now that we have the coordinates of the point on the unit circle, we can determine the sine of the angle. The sine of 120 degrees is equal to the y-coordinate of the point, which in this case is √3/2.

Therefore, sin(120°) = √3/2.

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