[funlearn] 三角函數講義Ans(一)
Post on 14-Oct-2014
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Fun Learn
1 AOB = 0o90oABCD( 1 ) sincostancotseccsc
Sol )(1)C E D A E
(2)C E D A E
O F B
O EF OE
FO
F B
O OF OE
F OF 1 = cos
=
EF 1
= sin
=
(3)C E D A A
(4)C EO F B AB OB
D
A
A
O
1 =
B
O F B= tan
O OA OB
1
B OA 1 = sec
AB 1
=
(5)C E D A O 1 D F B CD OC = CD 1 = cotC E D A O 1 D F B OD OC = OD 1 = csc
O
CO
C
4
Fun Learn
2sin 45 o sec 45 o + cos 30 o csc 60 o + tan 60 o cot 60 o =
Sol )= 2 2 3 2 1 + + 3 2 2 2 3 3 = 1+1+1 = 3
31 1 1 1 1 1 + + + + + = 1 + sin 1 + cos 1 + tan 1 + cot 1 + sec 1 + csc
Sol )= 1 1 1 1 1 1 + + + + + 1 + sin 1 + cos 1 + tan 1 + cot 1 + sec 1 + csc
=
1 1 1 + + + 1 + sin 1 + cos 1 + tan
1 1+ 1 tan
+ 1+
1 1 cos
+ 1+
1 1 sin
= =
1 1 1 tan cos sin + + + + + 1 + sin 1 + cos 1 + tan 1 + tan 1 + cos 1 + sin 1 + tan 1 + cos 1 + sin + + = 1+1+1 = 3 1 + tan 1 + cos 1 + sin
4sin 2 17 O + sin 2 73 O + tan 2 35 O cot 2 29 O sec 2 35 O + csc 2 29 O =
Sol )= sin 2 17 O + cos 2 17 O + (tan 2 35 O sec 2 35 O ) (cot 2 29 O csc 2 29 O ) = 1 + ( 1) ( 1) = 1
5
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