Finding the Value of cos 60°: Exploring Trigonometric Ratios and Special Angles

cos 60°

To find the value of cos 60°, we can use the unit circle or refer to the trigonometric ratios of special angles

To find the value of cos 60°, we can use the unit circle or refer to the trigonometric ratios of special angles. In this case, 60° is a special angle with a known value of the cosine.

The cosine function represents the ratio of the length of the adjacent side to the hypotenuse in a right triangle. To visualize this, let’s consider a right triangle where the angle 60° is one of the acute angles.

In this triangle, the adjacent side is the side nearest to the angle of 60°, and the hypotenuse is the longest side of the triangle. Let’s assume the length of the adjacent side is “x,” and the length of the hypotenuse is “1” (as the unit circle is a circle with a radius of 1).

By using the Pythagorean theorem, we can find the length of the opposite side, which is the square root of (1^2 – x^2).

Now applying the definition of cosine, cos 60° = adjacent/hypotenuse = x/1 = x.

To evaluate x, we can use the fact that 60° is also a special angle in an equilateral triangle, where all sides are equal. In this case, the adjacent side and the hypotenuse (also equal sides) are both “1/2” because the radius of the unit circle is 1 and we divide it by 2.

Since x = 1/2, the value of cos 60° can be concluded as 1/2. Therefore,
cos 60° = 1/2.

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