Understanding the Sine Function | Calculating sin(π/6) (30 degrees) in Mathematics

sin π/6 (30)

In mathematics, the sine function, denoted as sin(x), is a trigonometric function that relates the angle of a right triangle to the ratio of two sides

In mathematics, the sine function, denoted as sin(x), is a trigonometric function that relates the angle of a right triangle to the ratio of two sides. More specifically, for an angle x in radians, sin(x) is defined as the ratio of the length of the side opposite to the angle x to the length of the hypotenuse:

sin(x) = opposite / hypotenuse

In your question, sin π/6 (30), we are looking at the sine of the angle π/6 (which is equivalent to 30 degrees). To find this value, we first need to determine the ratio of the opposite side to the hypotenuse in a right triangle with a π/6 angle.

Let’s consider the unit circle which is a circle with a radius of 1 unit centered at the origin of a coordinate plane. When we draw a line from the origin to a point on the unit circle, the angle it makes with the positive x-axis is considered.

For the angle π/6 (30 degrees), if we draw a line from the origin to the point where the angle intersects the unit circle, the length of this line is the same as the opposite side of the right triangle. And since the radius of the unit circle is 1, the length of the hypotenuse is also 1.

So we have:

opposite = 1
hypotenuse = 1

Now, substituting these values into the sine formula:

sin(π/6) = opposite / hypotenuse = 1 / 1 = 1

Therefore, sin π/6 (30) = 1.

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