1.Solve cosx=sin2x
2.Find the value of sinxcosx when tanx=0.5
3.From a lighthouse L. a ship was spotted at P in the direction 046 degree.
The ship was sailing due west at a speed of 10km/h. Half an hourlater,
the ship was observed to be at Q in the direction 345 degree.
How far was Q from L?
THX~~
Help 3 math questions
2011-04-29 4:29 am
回答 (2)
2011-04-29 10:42 pm
✔ 最佳答案
1. cos x = sin 2x
cos x = cos (90 - 2x)
.......x = 90 - 2x
.....3x = 90
.......x = 30 deg
2.
tan x = 0.5 = 1/2
Draw right-angled triangle:
=> opposite side (對邊) = 1
=> adjacent side (鄰邊) = 2
==> hyp 斜邊 = root 5 (By Pyth Thm)
Therefore, sin(x) * cos(x) = (1/root5)*(2/root5) = 2/5
3.
Draw triangle LPQ.
(PQ 是一條橫線, Q 在左, P在右.)
(L在PQ下方)
(在 PQ大約中間的位置設一點 R , LR 垂直於PQ)
We have
(i) angle_PLR = 46 degree
(ii) angle_QLR = 360 - 345 = 45 degree
(iii) PQ = 10 * 1/2 = 5 km
.
In triangle PLR, PR = LR * tan 46
In triangle QLR, RQ = LR * tan 45
.
PQ = PR + RQ = LR * tan 46 + LR * tan 45 = LR * (tan 46 + tan 45)
LR = PQ/(tan 46 + tan 45) = 5 / (1.03553 + 1) = 2.45636
.
In triangle QLR, cos 45 = LR / QL
QL = LR / cos 45 = 2.45636 / 0.70711 = 3.47382
.
Therefore, QL is 3.47 km (corr to 3 sig fig)
2011-04-29 8:12 pm
=.=||
cosx=sin(90-x)
sin2x=cosx
so 2x=90-x
3x=90
x=30
sinxcosx
=2sin^2 x
=2(2tanx/[1+(tanx)^2])
=2(1/[1+0.25])
=2/1.25
=1.6
2011-04-29 12:12:24 補充：
3.從燈塔裡發現向着方向為046的船(L位)向正西的方向以速度10公里/小時行駛,半小時後船位於L位向345的方向角向着(Q位),求Q to L
2011-04-30 07:26:29 補充：
please choose 002
cosx=sin(90-x)
sin2x=cosx
so 2x=90-x
3x=90
x=30
sinxcosx
=2sin^2 x
=2(2tanx/[1+(tanx)^2])
=2(1/[1+0.25])
=2/1.25
=1.6
2011-04-29 12:12:24 補充：
3.從燈塔裡發現向着方向為046的船(L位)向正西的方向以速度10公里/小時行駛,半小時後船位於L位向345的方向角向着(Q位),求Q to L
2011-04-30 07:26:29 補充：
please choose 002
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