F.3三角比的關係

1. 2 tanθ/sinθ
=2(sinθ/cosθ)/sinθ
=2/cosθ
2. 3 sin2θ+3cos2θ
=3(sin2θ+cos2θ)
=3(1)
=3
3. -4cos2θ- 4sin2θ
=-4(sin2θ+cos2θ)
=-4(1)
=-4

4. tan2θcos2θ+cos2θ
=(sin2θ/cos2θ)cos2θ+cos2θ
=sin2θ+cos2θ
=1

5. 1/sinθ- cos2θ/ sinθ
=(1-cos2θ) /sinθ
=sin2θ/sinθ
=sinθ

6. 1/cos2θ- tan2θ
=1/cos2θ-(sin2θ/cos2θ)
=(1-sin2θ)/cos2θ
=cos2θ/cos2θ
=1

7. 3cosθ/sin(90-θ)
=3cosθ/cosθ
=3

8. sin(90-θ)/cos(90-θ)tanθ
=cosθ/sinθ(sinθ/cosθ)
=1
9. tanθ/cos(90-θ) - 1/sin(90-θ)
=(sinθ/cosθ)/sinθ-1/cosθ
=1/cosθ-1/cosθ
=0

求θ
1.tan58=1/tanθ
tan58=tan(90-θ)
58=90-θ
θ=32

求各題的值
1. sin2 27 + sin2 63
=sin2 27+cos2(90 -63)
=sin2 27+cos2 27
=1

2. tan32- 1/tan58
=tan32-tan(90-58)
=tan32-tan32
=0

3. tan18 tan72
=(tan18 )[1/tan(90 -72)]
=tan18(1/tan18)
=1

4. cos69/sin21
=sin(90 -69)/sin21
=sin21/sin21
=1


5.sin34 cos56+sin56 cos34
=sin(34+56)
=sin90
=1
6.若sinθ=3/5 ,求cosθ和tanθ的值。
cosθ=4/5
tanθ=3/4
7.若cosθ=5/7 ,求sinθ和tanθ的值。
sinθ=(√24)/7
tan=(√24)/5

求下題的θ
1.√2 sinθ=1
sinθ=1/√2
θ=45

2.1-sinθ=1/2
sinθ=1/2
θ=30

3.√3 tanθ=3
tanθ=3/√3
tanθ=√3
θ=60

4.√2 cosθ-1=0
cosθ=1/√2
θ=45