已知a是锐角,且sin(A减四分之派)等于五根号五,求SinA
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![已知a是锐角,且sin(A减四分之派)等于五根号五,求SinA](/uploads/image/z/1730181-21-1.jpg?t=%E5%B7%B2%E7%9F%A5a%E6%98%AF%E9%94%90%E8%A7%92%2C%E4%B8%94sin%28A%E5%87%8F%E5%9B%9B%E5%88%86%E4%B9%8B%E6%B4%BE%EF%BC%89%E7%AD%89%E4%BA%8E%E4%BA%94%E6%A0%B9%E5%8F%B7%E4%BA%94%2C%E6%B1%82SinA)
已知a是锐角,且sin(A减四分之派)等于五根号五,求SinA
已知a是锐角,且sin(A减四分之派)等于五根号五,求SinA
已知a是锐角,且sin(A减四分之派)等于五根号五,求SinA
根据A是锐角,那么A∈(0,π/2)
所以A-π/4∈(-π/4,π/4)
另外根据sin(A-π/4)=√5/5>0
所以A-π/4∈(0,π/4)
所以
cos(A-π/4)=2√5/5
所以
sinA=sin(A-π/4+π/4)
=sin(A-π/4)cos(π/4)+cos(A-π/4)sinπ/4
=(√5/5)(√2/2)+(2√5/5)(√2/2)
=3√10/10