又有數唔識啊,關於Trigonometry

2012-12-19 8:04 pm
有無高人可以叫下我點solve : cos (150+θ) = sin 120 where 0 is <= θ <= 180
更新1:

仲有兩題阿.... Given that 0<= θ <= 180 , solve the equation sin(2θ-60) = 1/2 If 0<= θ <= 360 and sinθ = cos110 , find θ

更新2:

我唔係好明點解.... -sin(60 + θ) = sin120 之後會變左....60 + θ = 240 or 300 點約ga....

回答 (2)

2012-12-19 10:38 pm
✔ 最佳答案
cos (150+θ) = sin 120

cos(90 + 60 + θ) = sin120

-sin(60 + θ) = sin120

60 + θ = 240 or 300

θ = 180

sin(2θ - 60) = 1/2 = sin30 or sin 150

2θ - 60 = 30 or 150

θ = 45 or 105

sinθ = cos110 = cos(90 + 20) = -sin20

θ = 200 or 340

2012-12-19 11:04 pm
cos(150 + θ) = sin120 = sin(180 - 120) = sin(60) = cos(90 - 60) = cos(30)
0 <= θ <= 180 -> 150 <= 150 + θ <= 330
150 + θ = 330 since 0 <= θ <= 180
θ = 180

0 <= θ <= 180
sin(2θ - 60) = 1/2 = sin(30)
0 <= θ <= 180 -> -60 <= 2θ - 60 <= 300
2θ - 60 = 30 or 150 since 0 <= θ <= 180
i.e. θ = 45 or 105

sinθ = cos110 = sin(90 - 110) = sin(-20)
θ = 180 - (-20) or θ = 360 + (-20) for 0 <= θ <= 360
θ = 200 or 340
參考: Myself - I'm lazy xD


收錄日期: 2021-04-27 17:44:53
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20121219000051KK00104

檢視 Wayback Machine 備份