cos θ formula
cos θ is one of the most commonly used trigonometric functions along with sin θ and tan θ. The cos θ is calculated in a right angle triangle which is defined as the ratio of the base to the hypotenuse of the right angle triangle.
The main functions in trigonometry are the rightangle triangle formulas. Cos θ is one of them. The main formula of cos θ is given by the ratio of base to the hypotenuse.
There are several identities relating to cos θ and other trigonometric functions. These include:

sin^{2} θ + cos^{2} θ = 1

cos θ = 1 / sec θ

cos θ = (1 – tan^{2} θ /2) / (1 + tan^{2} θ / 2)

cos θ = sin θ * cot θ

cos ( θ) = cos θ

cos (90 – θ) = sin θ

cos (180 + θ) = cos θ

cos (180 – θ) = – cos θ

cos 2 θ = cos^{2} θ – sin^{2} θ

cos (x + y) = cos x cos y – sin x sin y

cos (x – y) = cos x cos y + sin x sin y
Some solved examples
Q1. If sin θ = 6/ 13, find out the value of cos θ.
We know the formula that,
cos^{2} θ = 1 – sin^{2} θ
cos^{2 }θ = 1 – (6/ 13)^{2}
cos^{2} θ = 1 – 36/ 169
cos^{2} θ = 133/ 169
cos θ = (133)^{1/2}/ 13
Q2. If tan θ /2 = 5/ 8, find out the value of cos θ.
We know the formula that,
cos θ = (1 – tan^{2} θ /2) / (1 + tan^{2} θ /2)
cos θ = (1 – 25/ 64) / (1 + 25/ 64)
cos θ = (39/ 64) / (89/ 64)
cos θ = 39 / 89
Q3. Find cos θ if the value of sin θ = 2 / 5?
We know the formula that,
cos^{2} θ = 1 – sin^{2} θ
cos^{2} θ = 1 – (2 / 5)^{2}
cos^{2} θ = 1 – 4 / 25
cos^{2} θ = 16 / 25
cos θ = 4 / 5