1, addition rule: sin(a+b)=sinacosb+cosasinb, cos(a+b)=sinacosb-cosasinb, cos(a-b)=cosacosb+sinasinb, tan (a-b) = (tana-tanb).
2. multiplication rule: sin (a) × cos (b) = 0.5 sin (a+b)+sin (a-b), cos (a) × sin (b) = 0.5 sin (a+b)-sin (a-b), cos (a) × cos (b).
3. Division rule: sin(a)/cos(b)=tan(a), cos(a)/sin(b)=cot(b), cos(a)/cos(b)=-tan(a).
4. Half-angle formula: SIN (a/2) = √ (1-COSA)/2, COS (a/2) = √ (1+COSA)/2, TAN (a/2) = √ (1). These laws play a very important role in trigonometric function calculation, which can help us to carry out all kinds of complicated calculations and deductions.
The concept of trigonometric function
1, trigonometric function is a set of special functions in mathematics, which is related to the angle and side length of triangle. Specifically, trigonometric function is a function with angle as independent variable and real number or complex number as function value.
2. Trigonometric functions are usually represented by symbols such as sin, cos and tan. Among them, the sin function represents the sine value of an angle, that is, the area between the sine curve of the angle and the Y axis; Cos function represents the cosine value of an angle, that is, the area between the cosine curve of the angle and the y axis; The tan function represents the tangent value of the angle, that is, the area between the tangent curve of the angle and the X axis.
3. Trigonometric functions have some basic properties, such as periodicity, symmetry and parity. Among them, periodicity means that the value of trigonometric function appears repeatedly in a certain period; Symmetry means that trigonometric functions have symmetry at a certain angle, for example, sin(a) and sin(-a) are equal.
4. Parity means that trigonometric functions have parity at a certain angle, for example, sin(a) and cos(-a) are not equal. Trigonometric functions are widely used in mathematics, physics, engineering and other fields. For example, in geometry, trigonometric functions can be used to calculate angles, lengths and areas. In physics, trigonometric function can be used to describe vibration, wave and electromagnetic field.