Brief introduction of auxiliary angle formula;
1. Auxiliary angle formula is an advanced formula of a kind of trigonometric function proposed by Mr. Li, which is expressed as asinx+bcosx=√(a? +b？ )sin(x+φ)[a & gt； 0, φ=arctan(b/a)∈(-π/2, π/2)], the main function of this formula is to turn the sum of multiple trigonometric functions into a function, thus solving the maximum problem.
2, we need to analyze the meaning of each quantity in the formula, first look at the equation, the left two increase or decrease respectively, the sum of sine and cosine functions of a multiple. Look at the right side of the equation, a sine function, increase or decrease a certain multiple, the initial phase changes.
2. Presenter:
1, Li, original name Li, real name Qiu Xian, nickname Ren Shu. Born on181165438+122 October and died on1882 65438+9 February. He was a famous mathematician, astronomer, mechanic and botanist in modern China, and founded the power series expansion of quadratic root.
2. Studying the power series expansions of various trigonometric functions, anti-trigonometric functions and logarithmic functions, now called "natural number power sum formula", is the most significant achievement of Li and China's mathematics in19th century.