How to Calculate a Cosine

In any right triangle (a triangle that has one 90-degree angle), there are three sides and three angles. For any angle, the cosine is the measurement of the side adjacent to the angle over the hypotenuse, which is the side opposite the right angle. To calculate the cosine, you simply have to perform a division problem.

Things You'll Need

• Calculator

Instructions

1. Determine the length of the side adjacent to the angle in question; this is the side that is next to the angle but is not the hypotenuse.

2. Determine the length of the hypotenuse. If you do not know the hypotenuse's length, you can apply the Pythagorean theorem to find it. For this theorem, the hypotenuse equals the square root of the number you get when you add the squared lengths of the other two sides.

3. Divide the adjacent length by the hypotenuse length. This is the cosine of the angle in question.

Tips & Warnings

• Use the mnemonic device SOHCAHTOA to remember how to calculate sine, cosine and tangent. SOHCAHTOA reminds you that sine = opposite/hypotenuse, cosine = adjacent/hypotenuse and tangent = opposite/adjacent.

References

• Algebra Lab: Sine, Cosine, and Tangent