Как это подробно) cos(0.5arctg(8/15)-0.5pi)=? - вопрос №29841520581505 от coxa 20.01.2021 03:34

Question

Математика: Как это подробно) cos(0.5arctg(8/15)-0.5pi)=?

coxa · Answer

cos(0.5arctg(8/15)-0.5pi) - ?arctg(8/15) = x  уголtg(arctg(8/15)) = 8/15значит:a = 8  катетb = 15 катетc = √(8²+15²) = √(64+225) = √289 = 17 гипотенузах = arctg(8/15)  угол между b и ccos(0.5x-pi/2) = sin(0.5x) = = cos(0.5arctg(8/15)-0.5pi) = sin(0.5arctg(8/15))sin(x) = sin(arctg(8/15)) = 8/17cos(x) = cos(arctg(8/15)) = 15/17Формулa половинного аргумента:sin²(x/2) = (1 - cosx)/2sin²(x/2) = (1 - 15/17)/2sin²(x/2) = 1/17sin(x/2) =  ±1/√17 = ±√17/17sin(x/2) = sin(0.5arctg(8/15)) = cos(0.5arctg(8/15)-0.5pi)...