數學 <<基本三角學>>

1. 2 cos 3θ= tan 45
cos3θ=1/2
3θ=60
θ=30

2. tan 2θ = 1/2sin 60
2θ=√3 /4
2θ=23.4
θ=11.2


1. tan60 cos45/sin45
=tan60cot45
=(√3)(1)
=√3

2. cos2 30 - sin2 45 + cos 60
=(√3/2)2 - (1/2)2 + 1/2
=1

3. sin 60 cos 45 - cos 60 sin 45
=(√3/2)(√2/2)-(1/2)(√2/2)
=(√6-√2 )/4

4. (sin30 +sin 45)(tan60+1/tan30)
=[(1/2) +(√3/2)](√3+√3)
=[(1+√3)/2](2√3)
=√3+3

1.
2 cos 3θ= tan 45°
2 cos 3θ= 1
cos 3θ = 1/2
3θ=60°,300°,420°,660°,780°,1020°
θ=20°,100°,140°,220°,260°,340°//[[2兀n正負20°]]

2.
tan 2θ = 1/2sin 60°
tan 2θ = 1/開方3
2θ=30°,210°,390°,570°
θ=15°,105°,195°,285°//[[兀n+15°]]

2009-04-16 17:43:27 補充：
1.
tan60 cos45/sin45
tan60cot45
(√3)(1)
√3

2.
cos^2 30° - sin^2 45° + cos 60°
(√3/2)^2 - (√2/2)^2 + 1/2
(3/4)-(2/4)+(1/2)
3/4

3.
sin 60 cos 45 - cos 60 sin 45
(√3/2)(√2/2)-(1/2)(√2/2)
(√6-√2 )/4

4.
(sin30 +sin 45)(tan60+1/tan30)
[(1/2) +(√3/2)](√3+√3)
[(1+√3)/2](2√3)
√3+3