The trigonometric function value of the double angle 2α is expressed by some transformation relations of the trigonometric function value of the angle α, and the double angle formulas include sine double angle formula, cosine double angle formula and tangent double angle formula. It can be used to simplify the calculation formula and reduce the number of trigonometric functions in calculation, and it is also widely used in engineering.
Sin2α=2sinαcosα。 Cosine multiple angle formula: cos2α = (cosα) 2-(inα) 2; cos2α=2(cosα)^2- 1； cos2α= 1-2(sinα)^2。 Tangent dihedral formula: tan 2 α = 2 tan α/[ 1-(tan α) 2].
Trigonometric function is one of the basic elementary functions, which takes the angle (the most commonly used radian system in mathematics, the same below) as the independent variable, and the angle corresponds to the coordinates where the terminal edge of any angle intersects with the unit circle or its ratio as the dependent variable. It can also be equivalently defined as the lengths of various line segments related to the unit circle.
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. In mathematical analysis, trigonometric function is also defined as the solution of infinite series or specific differential equation, which allows its value to be extended to any real value or even complex value.
Application of Double Angle Formula
The application of double angle formula to the simplification, evaluation and proof of trigonometric function. Double angle formula is a set of formulas commonly used in mathematical trigonometric function. The trigonometric function value of double angle 2α is expressed by some transformation relations of trigonometric function value of angle α. In practical application, we should also pay attention to the various forms, flexible deformation and reverse use of the double-angle formula.
Only by mastering the double angle formula and its deformation formula skillfully can we use the formula flexibly. In the process of solving problems, the key is to grasp the relationship among the change of angles, the structure of shapes and names in formulas of trigonometric functions, use the unified thinking method of transformation, and flexibly use the double-angle formula.