Download - 已知三角函数值求角
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已知三角函数值求角
已知三角函数值求角已知三角函数值求角
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若 sinX= 求 X 。
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X
Y
O
sinX=
-1
1
当 X [- , ] 时 , X=
2
2
当 X [0 ,2 ] 时 , X=
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arcsin(- x )=-arcsin x , x [-1,1]∈
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若 sinX=0.7660 ,求 X 。
若 X=4, 求 X.若 X=10, 求 X.
Y=X
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X
Y
O2
2--
Y=sinX
1
-1
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X
Y
O
22
-
Y=sinX1
-1
2
2-
111-1
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函数 y =sin x
的反函数叫做反正弦函数:
记作 y =arcsin x ,x [-1,1]∈
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y =sin x y =arcsin x x∈[-1,1]
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arcsin(- x )=-arcsin x , x [-1,1]∈
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练习
( 1 ) arcsin 是什么意思? ( 2 )若 sinX=- ,X [- , ], 则 X=
( 3 )若 sinX=0.7, X [- , ], 则 X=
21
23
2
2 2
2
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X
Y
O2 π
Y=cosX
-1
1
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X
Y
O2 π
Y=cosX
-1
1
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( 2 )函数 y =cos x , x ∈[0, π ] 的反函数叫做反余弦函数:记作 y= arccosx , x
[-1,1] ∈
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y =cos x , x [0,∈ π ]
y= arccosx , x [-1,1]∈
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X
Y
O2 π
Y=cosX
-1
1
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( 1 )已知 X [0 , ],cosX=
0.7660, 求 X 。
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( 2 )已知 X [0 , ],cosX=
--0.7660, 求 X 。
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arccos(- x )= π -arccos x ,
x [-1,1]∈
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( 3 )已知 X [0 , 2 ],cosX=--0.7660, 求 X 。
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练习
( 1)X [0,2 ],cosX= , 求 X。( 2 )已知 X [0 , 2 ] cosX=cos61, 求 X 。 (3) 已知 X [0,2 ], cosX=sin30, 求 X
21
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sin(arcsin x )= x ________ cos(arccos x )= x________arcsin(sin x )= x_________
arccos(cos x )= x_________
1 寻求等式成立的条件
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sin(arcsin x )= x , x [-1,∈1]
cos(arccos x )= x , x [-1,∈1]arcsin(sin x )= x , x [- ,∈ ]
arccos(cos x )= x , x [0,∈ π ]
等式成立的条件
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二 . 求值1.sin(arcsin0.7660)=______2.cos[arccos(-0.3322)]=_____3.sin(arccos0.8)=_______4.cos(arcsin )=______
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arcsin(- x )=-arcsin x , x [∈-1,1]
arccos(- x )= π -arccos x , x [-1,1]∈
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X
Y
O2
2
-
1
-1
y =sin x y =arcsin x
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π X
Y
O2
-1
1
y =cos x y= arccosx
2
π
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