Trigonometry is a branch of mathematics that focuses on the relationships and calculations involving angles and triangles. It is used to solve problems related to measurements of sides and angles of triangles.
The cosine function (cos) is one of the primary trigonometric functions. It is used to calculate the ratio of the adjacent side to the hypotenuse in a right triangle. In other words, it represents the relationship between the length of the adjacent side and the length of the hypotenuse.
To find cos(a-b), you can use the trigonometric identity: cos(a-b) = cos(a)cos(b) + sin(a)sin(b). This means that you can multiply the cosines of the two angles and add the products of the sines of the two angles.
There is a difference in the calculation and meaning of these two expressions. Cos(a-b) is the cosine of the difference between two angles, while cos(a) - cos(b) is the difference between the cosines of two angles. It is important to understand the context in which these expressions are used to avoid confusion.
Trigonometry has many real-life applications, such as in architecture, engineering, navigation, and astronomy. It is used to calculate distances and heights, determine angles and directions, and solve problems related to waves and oscillations. It is also used in computer graphics and game development.