MindMap Gallery Trigonometric functions
Let junior high school students understand trigonometric functions. Trigonometric functions are a type of basic functions in mathematics, mainly including sine function (sin), cosine function (cos) and tangent function (tan).
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Trigonometric functions
1. Recommend listening to some songs
1.1. Song of Trigonometric Functions
2. definition
2.1. Trigonometric functions are a class of functions commonly used in mathematics, including sine, cosine, and tangent.
2.2. Trigonometric functions are periodic functions and have periodicity
3. nature
3.1. The range of trigonometric functions is 1,1
3.2. The period of a trigonometric function is 2π
3.3. Symmetries of Trigonometric Functions
4. application
4.1. Trigonometric functions play an important role in solving triangle problems
4.2. Trigonometric functions also play an important role in solving physical problems
5. Graphics of Trigonometric Functions
5.1. graph of sine function
5.1.1. The graph of the sine function changes periodically
5.1.2. The graph of the sine function is positive and negative symmetric
5.2. Graph of cosine function
5.2.1. The graph of the cosine function changes periodically
5.2.2. The graph of the cosine function is positive and negative symmetric
5.3. graph of tangent function
5.3.1. The graph of the tangent function changes periodically
5.3.2. The graph of the tangent function is positive and negative symmetric
6. Trigonometric formulas
6.1. sine formula
6.1.1. The sine formula is sin(A B)=sinAcosB cosAsinB
6.2. cosine formula
6.2.1. The cosine formula is cos(A B)=cosAcosBsinAsinB
6.3. tangent formula
6.3.1. The tangent formula is tan(A B)=(tanA tanB)/(1tanAtanB)
7. Derivation of Trigonometric Functions
7.1. Derivation of the sine formula
7.1.1. The sine formula is derived by addition and subtraction of vectors
7.2. Derivation of cosine formula
7.2.1. The cosine formula is derived by addition and subtraction of vectors
7.3. Derivation of tangent formula
7.3.1. The tangent formula is derived by addition and subtraction of vectors
8. Transformations of Trigonometric Functions
8.1. Transformations of trigonometric functions include addition and subtraction of trigonometric functions
8.2. Transformations of trigonometric functions include multiplication and division of trigonometric functions
8.3. Transformations of trigonometric functions include squares and square roots of trigonometric functions
9. Integrals of trigonometric functions
9.1. The integrals of trigonometric functions include the integrals of sine functions
9.2. The integrals of trigonometric functions include the integrals of cosine functions
9.3. The integrals of trigonometric functions include the integrals of tangent functions
10. Series of trigonometric functions
10.1. The series of trigonometric functions include the sine series
10.2. Series of trigonometric functions include cosine series
10.3. The series of trigonometric functions include tangent series
11. Applications of Trigonometric Functions
11.1. Application of trigonometric functions in solving trigonometric problems
11.2. Application of trigonometric functions in solving physical problems
11.3. Application of trigonometric functions in solving engineering problems
11.4. Application of Trigonometric Functions in Solving Economic Problems
11.5. Application of Trigonometric Functions in Solving Life Problems