Exploring the Cosine Function | Finding the Value of Cos 30° in a Right Triangle

cos 30°

The cosine function, denoted as cos, is a trigonometric function that relates the angle measures of a right triangle to the ratios of the sides of the triangle

The cosine function, denoted as cos, is a trigonometric function that relates the angle measures of a right triangle to the ratios of the sides of the triangle. In particular, cos(theta) represents the ratio of the length of the adjacent side to the hypotenuse of a right triangle, where theta is the angle between the adjacent side and the hypotenuse.

To find the value of cos 30°, we need to think of a right triangle with a 30° angle. Since we know that the sum of angles in a triangle is 180°, we can deduce that the other acute angle in this triangle is 60° (180° – 90° – 30°).

Now, let’s draw the right triangle and label the sides. We will call the side adjacent to the 30° angle as “a,” the side opposite to the 30° angle as “o,” and the hypotenuse as “h.”

o
/|
/ |
a/ | h
/ |
/____|
30°

Since we have the opposite and adjacent sides, we can now use the cosine function to find cos 30°. By the definition of cosine, we have:

cos 30° = adjacent side / hypotenuse = a / h

Now, let’s find the lengths of the sides of the triangle. The trigonometric ratios are usually used for right triangles with sides of length 1 (called unit triangles), so we can scale the sides of our triangle down by a factor of 2 to make the hypotenuse equal to 1. This means that a = 1/2 and h = 1.

Substituting these values into the cosine formula, we get:

cos 30° = (1/2) / 1

Simplifying, we find:

cos 30° = 1/2

Therefore, the value of cos 30° is equal to 1/2.

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