急! F5 Trigonometry 1

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2013-06-02 7:53 am

請詳細步教我做下條 :

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.

回答 (1)

Shu Fun

2013-06-02 5:34 pm

✔ 最佳答案

33.
(a) cos(2θ+60)° = -sin(2θ+k)°
cos(2θ+60)° = cos(90+2θ+k)°
2θ+60 = 90+2θ+k ± 360*n , where n is an integer
Since -90 ≦ k ≦ 90, k = -30

(b) From(a), cos(2θ+60)° = -sin(2θ-30)°
First contract the graph of y=sinθ along the axis of θ by half, becoming y=sin(2θ)
Then shift the graph 30 units to the right, becoming y=sin(2θ-30)°
Finally reflect the graph along the axis of θ, becoming y=-sin(2θ-30)°
Since cos(2θ+60)° = -sin(2θ-30)°, the graph of y=cos(2θ+60)° is obtained

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