1. Solving geometric problems: trigonometric functions can be used to solve geometric problems related to angles, lengths and areas. For example, sine theorem can be used to solve the relationship between the side length and angle of triangle; Cosine theorem can be used to solve the relationship between the side length and included angle of a triangle.
2. Describe the periodic phenomenon: trigonometric function has periodicity and can be used to describe the periodic phenomenon. For example, sine function can be used to describe periodic motion such as vibration and fluctuation; Cosine function can be used to describe periodic motion, such as rotation and oscillation.
3. Representing complex numbers: trigonometric functions can be used to represent complex numbers. For example, Euler's formula E (IX) = COSX+ISINX can convert real number X into complex number form, where E is the base of natural logarithm and I is imaginary unit.
4. Applied to physics: trigonometric functions are widely used in physics. For example, the voltage and current in AC circuit can be expressed by sine function; Interference and diffraction in optics can also be described by trigonometric functions.
In a word, trigonometric function is a very important function in mathematics and is widely used in many fields. By studying the properties and applications of trigonometric functions, we can better understand and solve various practical problems.