Bài 1 trang 153 sgk đại số 10
Bài 1 trang 153 sgk đại số 10 Bài 1. Tính ...
Bài 1 trang 153 sgk đại số 10
Bài 1. Tính
Bài 1. Tính
a) (cos {225^0},sin {240^0},cot( - {15^0}),tan{75^0});
b) (sin frac{7pi}{12}), (cos left ( -frac{pi}{12} ight )), ( anleft ( frac{13pi}{12} ight ))
Giải
a)
+) (cos{225^0} = cos({180^0} +{45^0})= - cos{45^{0}}= -frac{sqrt{2}}{2})
+) (sin{240^0} = sin({180^0} +{60^0}) = - sin{60^0}= -frac{sqrt{3}}{2})
+) (cot( - {15^0})= - cot{15^0} = - an{75^0} =- an({30^0} +{45^0}))
( =frac{- an30^{0}- an45^{0}}{1- an30^{0} an45^{0}}=frac{-frac{1}{sqrt{3}}-1}{1-frac{1}{sqrt{3}}}=-frac{sqrt{3}+1}{sqrt{3}-1}=-frac{(sqrt{3}+1)^{2}}{2} = -2 - sqrt 3)
+) ( an 75^0= cot15^0= 2 + sqrt3)
b)
+) (sin frac{7pi}{12} = sin left ( frac{pi}{3}+frac{pi}{4} ight ) =sinfrac{pi }{3}cosfrac{pi}{4}+ cos frac{pi }{3}sinfrac{pi}{4})
( =frac{sqrt{2}}{2}left ( frac{sqrt{3}}{2} +frac{1}{2} ight )=frac{sqrt{6}+sqrt{2}}{4})
+) (cos left ( -frac{pi }{12} ight ) = cos left ( frac{pi }{4} -frac{pi }{3} ight ) = cos frac{pi }{4}cosfrac{pi }{3} + sin frac{pi }{3}sin frac{pi }{4})
( =frac{sqrt{2}}{2}left ( frac{sqrt{3}}{2} +frac{1}{2} ight )=0,9659)
+) ( an left ( frac{13pi }{12} ight ) = an(π + frac{pi }{12}) = an frac{pi }{12} = an left ( frac{pi }{3}-frac{pi}{4} ight ))
(= frac{ anfrac{pi }{3}- anfrac{pi }{4}}{1+ anfrac{pi }{3} anfrac{pi }{4}}=frac{sqrt{3}-1}{1+sqrt{3}}= 2 - sqrt3)
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