Question

Упростите : СРОЧНО а) sin(a-90°); б)ctg(a-); в)ctg(a-360°); г) tg(-a+270°); д) (180°+a); е) ( 270°-a); ж) (90°+a); з) (360°-a); и) (270°+a).

Answer 1

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sin(-a) = - sina

cos(-a) = cosa

tg(-a) = - tga

ctg(-a) = - ctga

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Применяем формулы приведения:

а) sin( α - 90° ) = - sin( 90° - α ) = - cosα

б) ctg( α - π ) = - ctg( π - α ) = - ( - ctgα ) = ctgα

в) ctg( α - 360° ) = - ctg( 360° - α ) = - ( - ctgα ) = ctgα

г) tg( - α + 270° ) = tg( 270° - α ) = ctgα

д) sin²( 180° + α ) = sin²α

е) cos²( 270° - α ) = ( - sinα )² = sin²α

ж) tg²( 90° + α ) = ( - ctgα )² = ctg²α

з) ctg²( 360° - α ) = ( - ctg( 360° - α ) )² = ( - ( - ctgα ) )² = ctg²α

и) sin³( 270° + α ) = ( - cosα )³ = - cos³α

Answer 2

а) sin(a-90°) = sin(a) * cos(90°) - cos(a) * sin(90°) = sin(a) * 0 - cos(a) * 1 = -cos(a)

б) ctg(a-) = 1 / tan(a-) = 1 / tan(a)

в) ctg(a-360°) = 1 / tan(a-360°) = 1 / tan(a)

г) tg(-a+270°) = -tan(a-270°) = -tan(a)

д) (180°+a) = 180° + a

е) (+270°-a) = 270° - a

ж) (90°+a) = 90° + a

з) (360°-a) = 360° - a

и) (270°+a) = 270° + a