Формулы приведения

Рассмотрим рисунок:

Формулы приведения

На рисунке $begin mathsize 12px style angle X O M subscript 1 equals alpha semicolon end style$ $begin mathsize 12px style angle X O M subscript 2 equals pi over 2 alpha semicolon end style$ $begin mathsize 12px style M subscript 1 equals open parentheses c o s alpha semicolon s i n alpha close parentheses equals open parentheses x subscript 1 semicolon y subscript 1 close parentheses semicolon end style$ $begin mathsize 12px style M subscript 2 equals open parentheses c o s open parentheses pi over 2 plus alpha close parentheses semicolon s i n open parentheses pi over 2 plus alpha close parentheses close parentheses equals open parentheses plus y subscript 1 semicolon end subscript x subscript 1 close parentheses equals open parentheses negative s i n alpha semicolon space c o s alpha close parentheses end style$

Следовательно, справедливы формулы:

$begin mathsize 12px style c o s open parentheses pi over 2 plus alpha close parentheses equals negative s i n alpha semicolon space s i n open parentheses pi over 2 plus alpha close parentheses equals c o s alpha end style$

откуда вытекают формулы:

$size 12px t size 12px g open parentheses size 12px pi over size 12px 2 size 12px plus size 12px alpha close parentheses size 12px equals size 12px minus size 12px c size 12px t size 12px g size 12px alpha size 12px semicolon size 12px space size 12px c size 12px t size 12px g open parentheses size 12px pi over size 12px 2 size 12px plus size 12px alpha close parentheses size 12px equals size 12px minus size 12px t size 12px g size 12px alpha$

Если же в формулах (1) и (2) сделать замену: α на – α, то, воспользовавшись свойствами четности тригонометрических функций, мы получим формулы:

$begin mathsize 12px style c o s open parentheses pi over 2 minus alpha close parentheses equals s i n alpha semicolon space s i n open parentheses pi over 2 minus alpha close parentheses equals c o s alpha end style$

$size 12px t size 12px g open parentheses size 12px pi over size 12px 2 size 12px minus size 12px alpha close parentheses size 12px equals size 12px c size 12px t size 12px g size 12px alpha size 12px semicolon size 12px space size 12px c size 12px t size 12px g open parentheses size 12px pi over size 12px 2 size 12px minus size 12px alpha close parentheses size 12px equals size 12px t size 12px g size 12px alpha$

Полученные формулы называют формулами приведения.

В целом формулы приведения удобно представить в виде следующей таблицы.

Формулы приведения

Вопросы к конспектам

begin mathsize 12px style fraction numerator c o s squared alpha plus 2 s i n squared open parentheses alpha plus pi close parentheses over denominator c o s cubed open parentheses alpha minus 4 pi close parentheses end fraction plus fraction numerator c o s squared alpha plus 4 s i n alpha plus s i n squared open parentheses alpha plus pi close parentheses over denominator c o s alpha open parentheses 4 s i n alpha plus 1 close parentheses end fraction equals ? end style

size 12px с size 12px t size 12px g open parentheses size 12px 90 size 12px degree size 12px minus size 12px alpha close parentheses open square brackets size 12px c size 12px o size 12px s open parentheses size 12px 360 size 12px degree size 12px plus size 12px alpha close parentheses size 12px minus size 12px s size 12px i size 12px n size 12px alpha close square brackets size 12px plus fraction numerator size 12px s size 12px i size 12px n size 12px alpha size 12px plus size 12px t size 12px g size 12px alpha over denominator begin display style fraction numerator size 12px 1 over denominator size 12px s size 12px i size 12px n size 12px alpha end fraction size 12px plus size 12px c size 12px t size 12px g size 12px alpha end style end fraction size 12px equals size 12px ?

fraction numerator size 12px 2 size 12px minus begin display style fraction numerator size 12px 1 over denominator size 12px s size 12px i size 12px n to the power of size 12px 2 open parentheses begin display style size 12px pi over size 12px 2 size 12px plus size 12px alpha end style close parentheses end fraction end style over denominator size 12px 1 size 12px minus size 12px 2 size 12px c size 12px o size 12px s to the power of size 12px 2 open parentheses size 12px pi size 12px minus size 12px alpha close parentheses end fraction size 12px plus size 12px c size 12px t size 12px g to the power of size 12px 2 open parentheses size 12px pi over size 12px 2 size 12px minus size 12px alpha close parentheses size 12px equals size 12px ?

fraction numerator size 12px 2 size 12px c size 12px o size 12px s to the power of size 12px 2 size 12px alpha over denominator size 12px 1 size 12px minus size 12px s size 12px i size 12px n size 12px alpha end fraction size 12px plus size 12px 2 size 12px c size 12px o size 12px s open parentheses size 12px pi over size 12px 2 size 12px plus size 12px alpha close parentheses size 12px equals size 12px ?

fraction numerator size 12px t size 12px g open parentheses size 12px pi size 12px minus size 12px alpha close parentheses size 12px asterisk times size 12px c size 12px o size 12px s open parentheses size 12px minus size 12px alpha close parentheses over denominator size 12px s size 12px i size 12px n open parentheses begin display style size 12px pi over size 12px 2 size 12px minus size 12px alpha end style close parentheses end fraction size 12px equals size 12px ?

Error converting from MathML to accessible text.

Bычислите: ctg 40° tg140°

sin(-960°)=?

Последнее изменение: Воскресенье, 29 Январь 2017, 23:32