What is the Value of cos 180°

Q. What is the value of cos 180°?

Answer: The value of cos 180° is -1.

Trigonometry: The relationship between the sides and angles of triangles is the subject of this mathematical field. It literally means triangle measuring, but it has considerably more applications than that. It became a rigorous discipline in the 15th century when the need for precise surveying techniques and navigational methods led to its application in the “solution” of right triangles, or the calculation of the lengths of two sides of a right triangle given the length of one side and one of its acute angles. Ratios in the form of trigonometric functions can be used to find the solution.

One of the most widely used trigonometric functions is cosine (or Cos). The length, height, and angles of triangles are studied in trigonometry, a field of mathematics. Trigonometric functions are quite useful in the real world. Engineering, architecture, satellite navigation, medical imaging, and sound wave creation are only a few examples.

The ratio of a triangle’s adjacent side to its hypotenuse is known as cosine. We mostly deal with right-angle triangles in trigonometry. There is one right angle and two more angles that add up to 90 degrees. The Hypotenuse is the longest side opposite to the right angle, the Base or Adjacent is the bottom line, and the opposite is the perpendicular line segment. There are trigonometric identities based on these three ratios, such as sine, cosine, and tangent, among others.

Derivation of value cos 180° = -1

We can write,

 cos 180° = cos(270° – 90°)

cos 180°= – sin 90° cos 180° (⸪cos (270° – a) = – sin a)

Substitute the value of sin 90° which is 1 in the above relation, 

We get,

cos 180°= – (1) = -1

As a result, cos 180° is -1.