1, quotient relation formula:

The formula tanx=cosxsinx shows that the tangent function is a sine function divided by cosine function. Because the denominator cannot be 0, when x=2π+kπ(k is an integer), cosx=0, and tanx does not exist.

2. Sum and difference angle formula:

tan(x+y)= 1？ tanxtanytanx+tany .

sin(x+y)=sinxcosy+cosxsiny .

cos(x+y)=cosxcosy？ Cynthia.

These formulas are very useful in solving problems involving the sum and difference of angles.

3. Double angle formula:

tan2x= 1？ tan2x2tanx .

sin2x=2sinxcosx .

cos2x=cos2x？ sin2x .

These formulas are very useful in solving problems involving double angles.

4. Half-angle formula:

tan2x= 1+cosx 1？ cosx .

sin2x=2 1？ cosx .

cos2x=2 1+cosx .

These formulas are very useful in solving problems involving half angles.

Application in trigonometric function:

1, Physical Problems: In physics, many phenomena can be described by trigonometric functions. For example, the displacement, velocity and acceleration of simple harmonic vibration can be expressed as sine and cosine functions. The propagation of electromagnetic wave can be described by trigonometric function.

2. Geometry: In geometry, trigonometric functions are used to solve problems related to triangles. For example, trigonometric functions are often used to calculate the area, angle and side length of triangles.

3. Signal processing: In the field of signal processing, sine and cosine functions are the basic tools to describe periodic signals. Communication, audio processing, image processing and other fields all involve the spectrum analysis and filtering of signals, which requires the knowledge of trigonometric functions.

4. Engineering field: In civil engineering, mechanical engineering, aerospace engineering and other fields, the vibration, stability analysis and strength calculation of structures all involve the application of trigonometric functions.

5. Finance and economy: In the financial and economic fields, the changes of interest rates, exchange rates, stock prices and other variables can often be described and analyzed by sine and cosine functions.

6. Physical experiments: In physical experiments, it is often necessary to measure physical quantities such as angle and displacement, and the changes of these quantities can be described by trigonometric functions. For example, measuring the interference and diffraction of light requires the knowledge of trigonometric functions.