cos 30 degrees is a fundamental trigonometric value. In a 30-60-90 triangle,
the cosine of 30 degrees equals the adjacent side divided by the hypotenuse.
The exact value is square root of 3 over 2, which is approximately 0.866.
We can also understand cos 30 degrees using the unit circle.
On a circle with radius 1, the cosine of any angle equals the x-coordinate
of the corresponding point. At 30 degrees, the point has coordinates
square root 3 over 2 comma 1 over 2, confirming that cos 30 degrees equals square root 3 over 2.
To calculate the exact value, we start with an equilateral triangle.
When we draw a height from the top vertex to the base, it creates two identical
30-60-90 triangles. Using the Pythagorean theorem, the height equals square root of 3.
In the resulting right triangle, cos 30 degrees equals the adjacent side over the hypotenuse,
which is square root 3 over 2, approximately 0.866.
cos 30 degrees belongs to a group of special angles with exact values.
These include 0, 30, 45, 60, and 90 degrees. The table shows how cos 30 degrees
equals square root 3 over 2, while sin 30 degrees equals 1 over 2.
A useful memory tip is that 30-60-90 triangles have sides in the ratio 1 to square root 3 to 2.
To summarize, cos 30 degrees equals square root 3 over 2, which is approximately 0.866.
This value can be derived from the 30-60-90 triangle, represents the x-coordinate on the unit circle at 30 degrees,
and is one of the fundamental special angles in trigonometry. This value has important applications in physics,
engineering, mathematics, and computer graphics. Remember: cos 30 degrees equals square root 3 over 2.