1.Let tan x=t, where x lies between 90 and 180. Calculate, in terms of t, the value of sec x, cos x, sin x.
2.Giving your answer in the interval from -180 to 180, tan x=cos x, find x.
3.Giving your answer in the interval from -180 to 180, 2sec x=cosec x, find x.
數學: 3 trigonometry Q
2011-07-27 10:16 pm
回答 (2)
2011-07-27 10:27 pm
✔ 最佳答案
1) sec2 x = tan2 x + 1 = t2 + 1sec x = -√(t2 + 1) since sec x < 0 for 90 < x < 180
cos x = 1/sec x = -1/√(t2 + 1)
sin2 x = 1 - cos2 x = 1 - 1/(t2 + 1) = t2/(t2 + 1)
sin x = -t/√(t2 + 1) since sin x > 0 and t = tan x < 0 for 90 < x < 180
2) tan x = cos x
sin x = cos2 x
sin x = 1 - sin2 x
sin2 x + sin x - 1 = 0
sin x = (√5 - 1)/2 or -(√5 + 1)/2 (rej.)
x = 38.2 or 141.8
3) 2 sec x = csc x
2 sin x = cos x
tan x = 1/2
x = 26.6 or -153.4
參考: 原創答案
2011-07-28 12:04 am
收錄日期: 2021-04-13 18:07:34
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