Maths唔識抵死題(new)

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Keiis

2010-09-17 6:36 am

5c)

Find the values of sin x, cos x and tan x when x is acute and tan 2 x = 3/4.

SHow all, all all the steps

更新1:

can u leave it in surd form pls?? in square root

回答 (2)

Anonymous

2010-09-19 6:17 am

✔ 最佳答案

consider a right triangle obey tan 2x=3/4

it will have a hypotenuse=(3^2+4^2)^0.5
=5

so, cos2x=4/5
(cosx)^2-(sinx)^2=4/5
(cosx)^2-1+(cosx)^2=4/5
(cosx)^2=9/10
cosx=(9/10)^0.5 or cosx=-(9/10)^0.5 (rejected)
(sinx)^2=1-(cosx)^2
(sinx)^2=1/10
sinx=(1/10)^0.5 or sinx=-(1/10)^0.5(rejected)
tanx=sinx/cosx
=(9/10)^0.5/(1/10)^0.5
=1/(9^0.5)
=1/3

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Godfrey

2010-09-17 5:13 pm

Let k = 2x

Tan k = ¾ = 0.05
k = arctan(0.75) = 36.8698º

36.8698º = 2x
x = 36.8698º/2 = 18.43º

tan x = tan 18.43º = 0.3332

sin x = sin 18.43º = 0.3161

cos x = cos 18.43º = 0.9487

2010-09-17 09:16:02 補充：
correction:

tan k = 3/4 = 0.75 (0.05 is wrong; typo error)

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