Cosine Calculator, Formulas, Rules, and Examples

Cosine calculator

Hello engpocket friends, today we are going to talk about something very mathematics. It is cosine. From architecture to engineering to video game development, cosine function plays a vital role in calculating distances and angles.

Whether you are a student solving a geometry problem or a professional calculating the slope of a roof, or whatever job you are into, our cosine calculator is here to provide you instant and accurate results.

What is cosine?

In a right angled triangle, the cosine (cos) of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse (the longest side).

To memorize this easily, english speakers often use these easy words: SOH CAH TOA.

• SOH: Sine = Opposite / Hypotenuse
• CAH: Cosine = Adjacent / Hypotenuse
• TOA: Tangent = Opposite / Adjacent

The formula of cosine

This cosine formula is the same way as the cosine calculator works

$\begin{array}{l} \textbf{The Cosine Formula} \\ \cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}} \\[15pt] \textbf{Key Values to Remember:} \\ \cos(0^{\circ}) = 1 \\ \cos(60^{\circ}) = 0.5 \\ \cos(90^{\circ}) = 0 \end{array}$

Real world example of cosine calculation

A ladder in my project is leaning against a wall. The ladder is 10 meters long, this one is the hypotenuse). The angle between the ladder and the ground is 60 degrees. How far is the base of the ladder from the wall (adjacent side)? Help me calculate the cosine.

You can try to solve this with our cosine calculator too

$\begin{array}{l} \textbf{Given:} \\ \text{Hypotenuse } (H) = 10 \text{ m} \\ \text{Angle } (\theta) = 60^{\circ} \\[10pt] \textbf{The Solution:} \\ \text{We need to find the Adjacent side } (A). \\ \cos(60^{\circ}) = \frac{A}{10} \\[10pt] \text{Step 1: Substitute the value of } \cos(60^{\circ}) = 0.5 \\ 0.5 = \frac{A}{10} \\[10pt] \text{Step 2: Rearrange to solve for } A \\ A = 10 \times 0.5 \\ A = \mathbf{5 \text{ meters}} \\[10pt] \textbf{} \\ \text{} \end{array}$

Answer: The base of the ladder is 5 meters away from the wall in my project.

We also have a percentage calculator on this link other than this cosine calculator. On the next post, we will give you the sine calculator and we are sure that this will be very useful too. Goodbye and see you.