Understanding the value of cos 30°: Exploring the unit circle and trigonometric identities

cos 30°

To find the value of cos 30°, we can use the unit circle or the trigonometric identity for the cosine function

To find the value of cos 30°, we can use the unit circle or the trigonometric identity for the cosine function.

Using the unit circle:
The unit circle is a circle with a radius of 1 unit, centered at the origin of a coordinate plane. Each point on the unit circle corresponds to an angle measure in radians. At the point where the angle measures 30 degrees (or π/6 radians), the x-coordinate represents the value of cos 30°.

In the case of 30 degrees, the cosine function is positive in the first quadrant since the x-coordinate is positive. So, cos 30° = positive value.

Using the trigonometric identity:
The trigonometric identity for cos 30° is derived from the special right triangle called the 30-60-90 triangle. In this triangle, one of the acute angles is 30 degrees, and the sides are in the ratio 1:√3:2.

In the 30-60-90 triangle, the side opposite the 30-degree angle has a length of 1, and the hypotenuse has a length of 2. Since cos(theta) is defined as the adjacent side divided by the hypotenuse, we divide 1 by 2 to find cos 30°.

cos 30° = 1/2

So, cos 30° = 1/2 or approximately 0.5.

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