已知函数f(x)={1-[(√2)sin(2x-π/4)]}/cosx (1)求f(x)的定义域(2)设α是第四象限的角,且tanα=-4/3,求f(α)的值.
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![已知函数f(x)={1-[(√2)sin(2x-π/4)]}/cosx (1)求f(x)的定义域(2)设α是第四象限的角,且tanα=-4/3,求f(α)的值.](/uploads/image/z/8626520-56-0.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3D%7B1-%5B%28%E2%88%9A2%29sin%282x-%CF%80%2F4%29%5D%7D%2Fcosx+%EF%BC%881%EF%BC%89%E6%B1%82f%28x%29%E7%9A%84%E5%AE%9A%E4%B9%89%E5%9F%9F%EF%BC%882%EF%BC%89%E8%AE%BE%CE%B1%E6%98%AF%E7%AC%AC%E5%9B%9B%E8%B1%A1%E9%99%90%E7%9A%84%E8%A7%92%2C%E4%B8%94tan%CE%B1%3D-4%2F3%2C%E6%B1%82f%28%CE%B1%29%E7%9A%84%E5%80%BC.)
已知函数f(x)={1-[(√2)sin(2x-π/4)]}/cosx (1)求f(x)的定义域(2)设α是第四象限的角,且tanα=-4/3,求f(α)的值.
已知函数f(x)={1-[(√2)sin(2x-π/4)]}/cosx
(1)求f(x)的定义域
(2)设α是第四象限的角,且tanα=-4/3,求f(α)的值.
已知函数f(x)={1-[(√2)sin(2x-π/4)]}/cosx (1)求f(x)的定义域(2)设α是第四象限的角,且tanα=-4/3,求f(α)的值.
(1)cosx≠0
x≠Kπ+π/2 K∈Z
(2)由tanα=-4/3可知:sinα=4/5,cosα=-3/5
得:sin2α=2sinα*cosα=-24/25
cos2α=1-2(sinα)^2=-7/25
f(α)=[1-√2sin(2α-π/4)]/cosα
=[1-√2(sin2α*cosπ/4-cos2α*sinπ/4)]/cosα
=[1-sin2α+cos2α]/cosα
=[1+24/25-7/25]/(-3/5)
=-14/5
(1)
f(x)={1-[(√2)sin(2x-π/4)]}/cosx
f(x) define over real number except
cosx = 0
x = (2k+1)π/2 , k =0,±1,±2,....
f(x)的定义域
= R / A
where A = {(2k+1)π/2 , k =0,...
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(1)
f(x)={1-[(√2)sin(2x-π/4)]}/cosx
f(x) define over real number except
cosx = 0
x = (2k+1)π/2 , k =0,±1,±2,....
f(x)的定义域
= R / A
where A = {(2k+1)π/2 , k =0,±1,±2,....}
(2)
tanα=-4/3
sinα = -4/5
cosα = 3/5
f(α))={1-[(√2)sin(2α-π/4)]}/cosα
= {1- (1/2)( sin2α - cos2α)} / cosα
= { 1- (1/2)( 2sinαcocosα - [cosα]^2+ [sinα]^2 } / cosα
= { 1- (1/2) ( 2(-12/25) - 9/25 + 16/25 }/ (3/5)
= {1+ (1/2) (17/25) } /(3/5)
= (67/50) ( 5/3)
= 201/10
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