有關函數既問題!!!!(20點)

2010-10-12 2:39 am

如題,,thx very much^^

1.若f(θ)=cosθ,其中0°≦θ≦90°,求下列各值
a.f(30°) b.f(45°) c.f(60°)

2.若f(x)=x(x+1),求下列各值
a.2f(-4) b.f(2)+[f(-3)]^2

3.若f(t)=t^2+1及g(t)=2t,求下列各值
a.g(3)+f(0) b.f(1)‧g(-1) c.g(-4)/f(3)

更新1:

第一題全部都係小過或等於零

回答 (1)

知識就是力量

2010-10-12 4:52 am

✔ 最佳答案

1a. f(30°) = cos 30° = √3 / 2
b. f(45°) = cos 45° = √2 / 2
c. f(60°) = cos 60° = 1 / 2

2a. 2f(-4) = 2[-4(-4+1)] = 24
b. f(2) + [f(-3)]^2
= 2(2+1) + [-3(-3+1)]^2
= 6 + 6^2
= 42

3a. g(3) + f(0)
= 2(3) + (0^2 + 1)
= 6 + 1
= 7
b. f(1) * g(-1)
= (1^2 + 1) * 2(-1)
= 2*(-2)
= -4
c. g(-4)/f(3)
= 2(-4) / (3^2 + 1)
= -8 / 10
= -4/5

2010-10-11 20:55:45 補充：
第一題a,b,c沒可能小過零
若0 =< θ =< 90, 其cosθ數值的範圍只會由0到1
請參考http://www.gcsemathstutor.com/images/algebra/cosgraphtransform1.jpg

參考: Knowledge is power.

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