1. Solve √3 + 2cosx = 0, where 0°≤ x < 360°.
2. Solve 2cosθ + 1 = 0, where 0°≤ x < 360°.
3. Solve 3tanθ - √3 = 0, where 0°≤ x < 360°.
4. Solve tan²x + 2tanx - 24 = 0 for 0°≤ x < 360°.
5. Solve 1 - cosθ= sin²θ, where 0°≤ x < 360°.
6. Solve (7sinθ + cosθ)/(4sinθ + cosθ) = 2, where 0°≤ x < 360°.
7a. Rewrite 8tanθ = 3cosθ in the form xsin²θ + ysinθ + z = 0, where x, y and z are integers.
7b. Hence, solve the equation in (a) for 0°≤ θ ≤ 360°.
8. The figure below shows the graph of y = asinθ + k, find the value of a and k.
9. Find the maximum value and minimum value of each of the following trigonometric functions.
(a) 2 + 3cos(x + 45°)
(b) (-2/3) - 2cos3x
Steps and Ans Thank you very much!
Maths about Trigonometry
2014-08-05 11:37 pm
回答 (2)
2014-08-06 1:56 am
✔ 最佳答案
1.√3 + 2 cos x = 0
2 cos x=-√3
cos x=-(√3)/2
x=150 or x=210
2.
2 cosθ + 1 = 0
2 cosθ=-1
cosθ=-0.5
θ=120 or θ240
3.
3 tanθ - √3 = 0
tanθ=(√3)/3
θ=30 or 210
4.
tan²x + 2tanx - 24 = 0
tan x=4 or tan x=-6
x=75.96375653 or x=255.9637565 or x=279.4623222 or x=99.46232221
5.
1 - cosθ= sin²θ
1-sin²θ=cosθ
cos²θ-cosθ=0
cosθ=0 or cosθ=1
θ=90 or θ=270 or θ=0
6.
(7 sinθ + cosθ)/(4 sinθ + cosθ) = 2
7 sinθ+cosθ=8 sinθ+2 cosθ
-sinθ=cosθ
tanθ=-1
θ=315 or θ=135
7 a.
8 tanθ = 3 cosθ
8 sinθ=3 cos²θ
3 cos²θ-8 sinθ=0
3(1-sin²θ)-8 sinθ=0
-3 sin²θ-8 sinθ+3=0
3 sin²θ+8 sinθ-3=0
7 b.
3 sin²θ+8 sinθ-3=0
sinθ=1/3 or sinθ=-3 (Delete)
θ=19.47122063 or 160.5287794
8.
No figure
9 a.
-1≤cos(x+45°)≤1
-3≤3 cos(x+45°)≤3
-1≤2+ cos(x+45°)≤5
9 b.
-1≤cos3x≤1
-2≤-2cos3x≤2
-(8/3)≤ (-2/3) - 2cos3x≤(4/3)
2014-08-05 18:04:57 補充：
To 土扁:
5.
1- cos 180°=2
sin² 180°=0
1- cos 180° 不等於 sin² 180°
2014-08-06 8:13 am
原來的答案沒有 180°，但最後一時糊塗加上了。
既然如此，把答案刪掉算了。
2014-08-06 00:15:47 補充：
嚴格來說，fighting gravity 全部答案可以說是錯的。
x = 150 或 x = 210 的意思是：
x = 150 radians 或 x = 210 radians
2014-08-06 00:16:43 補充：
當然，x = 0 是正確的。
既然如此，把答案刪掉算了。
2014-08-06 00:15:47 補充：
嚴格來說，fighting gravity 全部答案可以說是錯的。
x = 150 或 x = 210 的意思是：
x = 150 radians 或 x = 210 radians
2014-08-06 00:16:43 補充：
當然，x = 0 是正確的。
收錄日期: 2021-04-15 16:07:10
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20140805000051KK00083