標題:
發問:
1)sin(270-θ)．sin(180+θ) / tan(180+θ) 答案~cos^2θ 2)証明tan(90+θ)= -1/tanθ 3)不使用計算機,求下列的值 cos240度 除以 tan315度 答案~1/2 4)已知tanθ=-9/40及cosθ>0,試不求θ值而找出sinθ及cosθ的值 sinθ= -9/41 cosθ=40/41 5)求下列的θ值,其中90度<θ<270度(答案準確至3位有效數字) a)tanθ=2.75 答案~250.02度 b)sinθ=0.25 答案~165.52度 更新: 6)解下列方程,其中0度 更新 2: 6)解下列方程,其中0度 更新 3: 第6題取消!!請列出詳細,清楚ge步驟!!5該晒
最佳解答:
1)sin(270-θ)．sin(180+θ) / tan(180+θ) =-cosθ ． -sinθ / tanθ =cosθsinθ / (sinθ/cosθ) =cosθsinθ ． (cosθ / sinθ) =cos^2 θ 2)証明tan(90+θ)= -1/tanθ tan(90 + θ) = sin(90 + θ) /cos(90 + θ) = cosθ / -sinθ = -(1/sinθ/cosθ) = -1/tanθ 3)不使用計算機,求下列的值 cos240度 除以 tan315度 =cos(360 - 240)/tan(360 - 315) =cos120 / tan(-45) =cos(180 - 120) / -1 =-cos60 / -1 = 1/2 4)已知tanθ=-9/40及cosθ>0,試不求θ值而找出sinθ及cosθ的值 if tanθ=-9/40 r = sqrt(9^2 + 40^2) =41 sinθ= x/r =-9/40 cosθ=y/r =40/41 5)求下列的θ值,其中90度<θ<270度(答案準確至3位有效數字) a)tanθ=2.75 tanθ = 2.75 θ = 70.02 because 90度<θ<270度 so θ = 180 + 70.02 =250.02 b)sinθ=0.25 sinθ=0.25 θ=14.48 because 90度<θ<270度 so θ = 180 - 14.48 =165.52 2008-02-10 17:41:14 補充： 3)不使用計算機,求下列的值cos240度 除以 tan315度=cos(360 - 240)/tan(360 - 315)(*)=cos120 / -tan(45)=cos(180 - 120) / -1=-cos60 / -1= 1/2(*) is the correct step...SOR 2008-02-10 17:42:17 補充： sqrt(9^2 40^2)= 開方 (9^2 40^2)
其他解答:
some good: some bad!|||||1. sin(270-x) = sin(180+90-x)= -sin(90-x) = - cos x sin(180+x) = -sin x tan(180+x) = tan x sin(270-x)*sin(180+x)/tan(180+x) = (-cos x)(-sin x)/(tan x) = (-cos x)(-sin x)/(sin x/cox x) = (cos x)^2 2. tan(90+x)=sin(90+x)/cos(90+x)=sin(180-(90-x)/cos(180-(90-x))=sin(90-x)/-cos(90-x) =cos x/-sin x = -1/tan x 3. cos 240=cos(180+60)=cos 60 = 0.5 tan 315 = tan(360-45)= - tan 45 = -1 cos40/tan315= 0.5/-1 = -0.5 4. tan x = -9/40= opposite/adjecent tan is -ve, therefore either 2nd or 4th quad. cos >0 therefore 4th quad. so opposite side = -9 and adjacent side = 40 so hypotenus = (9^2+40^2)^0.5 = 41 sin x = opposite/hypotenus -9/41 and cos x = adjacent/hypotenus = 40/41 5.a) tan x = 2.75 ===========> x = 180 + 70.02 = 250.02 (tan +ve, 3rd quad) 5.b) sin x = 0.25 ===========> x = 180 - 14,48 =165.52 (sin +ve, 2nd quad) 2008-02-10 21:50:24 補充： error in 3.The correct solution is as follows3.cos 240=cos(180+60)=- cos 60 = -0.5tan 315 = tan(360-45)= - tan 45 = -1cos40/tan315= -0.5/-1 = 0.5
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中4__續3角的題目發問:
1)sin(270-θ)．sin(180+θ) / tan(180+θ) 答案~cos^2θ 2)証明tan(90+θ)= -1/tanθ 3)不使用計算機,求下列的值 cos240度 除以 tan315度 答案~1/2 4)已知tanθ=-9/40及cosθ>0,試不求θ值而找出sinθ及cosθ的值 sinθ= -9/41 cosθ=40/41 5)求下列的θ值,其中90度<θ<270度(答案準確至3位有效數字) a)tanθ=2.75 答案~250.02度 b)sinθ=0.25 答案~165.52度 更新: 6)解下列方程,其中0度 更新 2: 6)解下列方程,其中0度 更新 3: 第6題取消!!請列出詳細,清楚ge步驟!!5該晒
最佳解答:
1)sin(270-θ)．sin(180+θ) / tan(180+θ) =-cosθ ． -sinθ / tanθ =cosθsinθ / (sinθ/cosθ) =cosθsinθ ． (cosθ / sinθ) =cos^2 θ 2)証明tan(90+θ)= -1/tanθ tan(90 + θ) = sin(90 + θ) /cos(90 + θ) = cosθ / -sinθ = -(1/sinθ/cosθ) = -1/tanθ 3)不使用計算機,求下列的值 cos240度 除以 tan315度 =cos(360 - 240)/tan(360 - 315) =cos120 / tan(-45) =cos(180 - 120) / -1 =-cos60 / -1 = 1/2 4)已知tanθ=-9/40及cosθ>0,試不求θ值而找出sinθ及cosθ的值 if tanθ=-9/40 r = sqrt(9^2 + 40^2) =41 sinθ= x/r =-9/40 cosθ=y/r =40/41 5)求下列的θ值,其中90度<θ<270度(答案準確至3位有效數字) a)tanθ=2.75 tanθ = 2.75 θ = 70.02 because 90度<θ<270度 so θ = 180 + 70.02 =250.02 b)sinθ=0.25 sinθ=0.25 θ=14.48 because 90度<θ<270度 so θ = 180 - 14.48 =165.52 2008-02-10 17:41:14 補充： 3)不使用計算機,求下列的值cos240度 除以 tan315度=cos(360 - 240)/tan(360 - 315)(*)=cos120 / -tan(45)=cos(180 - 120) / -1=-cos60 / -1= 1/2(*) is the correct step...SOR 2008-02-10 17:42:17 補充： sqrt(9^2 40^2)= 開方 (9^2 40^2)
其他解答:
some good: some bad!|||||1. sin(270-x) = sin(180+90-x)= -sin(90-x) = - cos x sin(180+x) = -sin x tan(180+x) = tan x sin(270-x)*sin(180+x)/tan(180+x) = (-cos x)(-sin x)/(tan x) = (-cos x)(-sin x)/(sin x/cox x) = (cos x)^2 2. tan(90+x)=sin(90+x)/cos(90+x)=sin(180-(90-x)/cos(180-(90-x))=sin(90-x)/-cos(90-x) =cos x/-sin x = -1/tan x 3. cos 240=cos(180+60)=cos 60 = 0.5 tan 315 = tan(360-45)= - tan 45 = -1 cos40/tan315= 0.5/-1 = -0.5 4. tan x = -9/40= opposite/adjecent tan is -ve, therefore either 2nd or 4th quad. cos >0 therefore 4th quad. so opposite side = -9 and adjacent side = 40 so hypotenus = (9^2+40^2)^0.5 = 41 sin x = opposite/hypotenus -9/41 and cos x = adjacent/hypotenus = 40/41 5.a) tan x = 2.75 ===========> x = 180 + 70.02 = 250.02 (tan +ve, 3rd quad) 5.b) sin x = 0.25 ===========> x = 180 - 14,48 =165.52 (sin +ve, 2nd quad) 2008-02-10 21:50:24 補充： error in 3.The correct solution is as follows3.cos 240=cos(180+60)=- cos 60 = -0.5tan 315 = tan(360-45)= - tan 45 = -1cos40/tan315= -0.5/-1 = 0.5
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