# Caculatecos (θ)

θ angle

cos(θ)

In a right angled triangle, Cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.

## Formula

To find the Cosine of a given angle θ , use the following formula.

## Calculating Cos of an Angle

The cosine (cos) of an angle in a right triangle is a trigonometric function that represents the ratio of the length of the adjacent side to the hypotenuse. It is an important function in trigonometry, often used to find unknown side lengths or angles in right triangles.

The cosine of an angle \( \theta \) is defined as:

\( \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \)

where:

**adjacent**is the length of the side adjacent to angle \( \theta \).**hypotenuse**is the length of the hypotenuse (the side opposite the right angle).

### Example 1

Let's calculate the cosine of a 30-degree angle:

In a right triangle, if the angle \( \theta = 30^{\circ} \), the adjacent side is \( \sqrt{3} \) times half the length of the hypotenuse. So, the cosine of 30 degrees is:

\( \cos(30^{\circ}) = \frac{\sqrt{3}}{2} \approx 0.866 \)

### Example 2

Consider another example with a 45-degree angle:

In a right triangle, if the angle \( \theta = 45^{\circ} \), the adjacent side and the opposite side are of equal length, and the hypotenuse is \( \sqrt{2} \) times the length of the adjacent side. So, the cosine of 45 degrees is:

\( \cos(45^{\circ}) = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2} \approx 0.707 \)

These examples demonstrate how to calculate the cosine of an angle manually, showing the importance of understanding the trigonometric function cosine in various mathematical and practical applications.