急! F5 Trigonometry 問題1條唔明唔識做 ?

Bid

2013-05-31 6:59 am

請詳細解答下條做法的原因. 33(a) If cos(2θ+60)度≡-sin(2θ+k)度,where -90≦k≦90, find k(b) Hence describe the way of transformingthe graph of y=sinθ to the graph of y=cos(2θ+60) 度. 答案 :(a) cos(2θ+60)度=-sin(90-2θ-60)度 [點解(2θ+k)變為(90-2θ-60)] =sin(30-2θ) =-sin(2θ-30) 度 k=-30 [點計出這個答案,要步驟](b) 唔明 ?

回答 (1)

用戶10012

2013-05-31 3:21 pm

✔ 最佳答案

(a)
- sin (2x + k) = sin [ - (2x + k)] = sin (- 2x - k) = cos [ 90 - ( - 2x - k)]
= cos ( 90 + 2x + k) = cos (2x + 60)
so 90 + 2x + k = 2x + 60
k = 60 - 90 = - 30.
(b)
y = cos ( 2x + 60) = - sin ( 2x - 30)
Transformation :
(1) shift y = sin x to the right by 30 degree to get y = sin ( x - 30).
(2) reduce x by 1/2 ( that is reduce the period from 360 degree to 180 degree) to get y = sin (2x - 30)
(3) " Reverse " the curve upside down ( that is +ve becomes -ve and -ve becomes +ve) to get y = - sin (2x - 30) which is the same as y = cos (2x + 60)

2013-05-31 07:29:30 補充：
For part (b), alternate way to do is : (1) reduce x by 1/2 to get y = sin 2x. (2) shift it to the right by 15 degree to get y = sin 2(x - 15) = sin (2x - 30) then (3) reverse it.

👍 0 👎 0