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
Maths唔識抵死題(new)
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
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
回答 (2)
2010-09-19 6:17 am
✔ 最佳答案
consider a right triangle obey tan 2x=3/4it 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
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)
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)
收錄日期: 2021-04-23 20:45:41
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