The content of trigonometric function is called the chapter with the most formulas in high school. Indeed, there are many formulas, but they are all the same. The next content will be composed of basic formula, graphic memory, chapter summary+mind map. Let's learn trigonometric function together!
The trigonometric sum formulas of trigonometric functions are:
sin(α+β+γ)= sinαcosβcosγ+cosαsinβcosγ+cosαcosβsinγ-sinαsinβsinγcos(α+β+γ)= cosαcosβcosγ-cosαsinγ-sinαcosβsinγ-sinαsinβcosγtan(α+β+γ) =(tanα+tanβ+tanγ-tanαtanβtanβtanγ)/( 1-tanαtanβtanγtanγ-tanγtanγtanα。
The formulas of trigonometric functions of the sum and difference of two angles is:
cos(α+β)= cosαcosβ-sinαsinβcos(α-β)= cosαcosβ+sinαsinβsin(αβ)= sinαcosβcosαsinβtan(α+β)=(tanα+tanβ)/( 1-tanαtanβ)=(tanα-tanβ)/( 1+tanαtanβ)。
Definition of trigonometric function:
Trigonometric function is one of the basic elementary functions, which takes angle (the most commonly used radian system in mathematics, the same below) as the independent variable, and the coordinates of the intersection point between the terminal edge of any angle and the unit circle or its ratio as the dependent variable.
The trigonometric function relates the internal angle of a right triangle to the ratio of its two sides, and can also be defined by the lengths of various line segments related to the unit circle equivalently. Trigonometric function plays an important role in studying the properties of geometric shapes such as triangles and circles, and is also a basic mathematical tool for studying periodic phenomena.
From the 5th century to12nd century, Indian mathematicians made great contributions to trigonometry. Although trigonometry was still a computing tool and an accessory of astronomy at that time, the content of trigonometry was greatly enriched through the efforts of Indian mathematicians. The concepts of sine and cosine in trigonometry were first introduced by Indian mathematicians, who also made sine tables more accurate than Ptolemy.