Understanding the Sine Function and Calculating sin 60 Degrees

sin 60°

The sine of 60 degrees, denoted as sin 60°, is equal to 0

The sine of 60 degrees, denoted as sin 60°, is equal to 0.866025404.

To calculate the sine of an angle, you can use a scientific calculator or refer to a trigonometric table. However, it is helpful to understand the concept behind the sine function and its relationship to the unit circle.

The unit circle is a circle with a radius of 1 unit, centered at the origin of a coordinate plane. In the unit circle, the angle is measured in degrees or radians, starting from the positive x-axis and rotating counterclockwise.

To find the sine of 60 degrees, we can refer to the unit circle. At 60 degrees, the angle forms an equilateral triangle with the x-axis and a radius of the unit circle. This triangle has sides of equal length.

Since an equilateral triangle has three equal angles, each angle in the equilateral triangle formed at 60 degrees measures 60 degrees as well. In this triangle, the opposite side of the angle measured at 60 degrees is equal to half the length of the hypotenuse.

Using the Pythagorean theorem, we can determine the length of the opposite side as follows:

opposite^2 + adjacent^2 = hypotenuse^2
opposite^2 + (1)^2 = (2)^2
opposite^2 + 1 = 4
opposite^2 = 3

Taking the square root of both sides gives us:

opposite = √3

Therefore, the length of the opposite side, when the angle measures 60 degrees in the unit circle, is √3.

Now, we can calculate the sine of 60 degrees using the definition of the sine function:

sin 60° = opposite/hypotenuse
= (√3)/2

After simplifying, we get:

sin 60° = 0.866025404

So, the sine of 60 degrees is approximately equal to 0.866025404.

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