作业帮三角恒等变换题1.已知函数f﹙x﹚=a﹙cos²x＋sinxcosx﹚＋b（1）当a＞0时,求f﹙x﹚的单调增区间（2）当a＜0且x∈[0,兀／2]时,f﹙x﹚的值域是[3,4]求a,b的值.
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![三角恒等变换题1.已知函数f﹙x﹚=a﹙cos²x＋sinxcosx﹚＋b（1）当a＞0时,求f﹙x﹚的单调增区间（2）当a＜0且x∈[0,兀／2]时,f﹙x﹚的值域是[3,4]求a,b的值.](/uploads/image/z/7210660-4-0.jpg?t=%E4%B8%89%E8%A7%92%E6%81%92%E7%AD%89%E5%8F%98%E6%8D%A2%E9%A2%981.%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%EF%B9%99x%EF%B9%9A%3Da%EF%B9%99cos%26%23178%3Bx%EF%BC%8Bsinxcosx%EF%B9%9A%EF%BC%8Bb%EF%BC%881%EF%BC%89%E5%BD%93a%EF%BC%9E0%E6%97%B6%2C%E6%B1%82f%EF%B9%99x%EF%B9%9A%E7%9A%84%E5%8D%95%E8%B0%83%E5%A2%9E%E5%8C%BA%E9%97%B4%EF%BC%882%EF%BC%89%E5%BD%93a%EF%BC%9C0%E4%B8%94x%E2%88%88%5B0%2C%E5%85%80%EF%BC%8F2%5D%E6%97%B6%2Cf%EF%B9%99x%EF%B9%9A%E7%9A%84%E5%80%BC%E5%9F%9F%E6%98%AF%5B3%2C4%5D%E6%B1%82a%2Cb%E7%9A%84%E5%80%BC.)
三角恒等变换题1.已知函数f﹙x﹚=a﹙cos²x＋sinxcosx﹚＋b（1）当a＞0时,求f﹙x﹚的单调增区间（2）当a＜0且x∈[0,兀／2]时,f﹙x﹚的值域是[3,4]求a,b的值.
三角恒等变换题
1.已知函数f﹙x﹚=a﹙cos²x＋sinxcosx﹚＋b
（1）当a＞0时,求f﹙x﹚的单调增区间
（2）当a＜0且x∈[0,兀／2]时,f﹙x﹚的值域是[3,4]求a,b的值.
三角恒等变换题1.已知函数f﹙x﹚=a﹙cos²x＋sinxcosx﹚＋b（1）当a＞0时,求f﹙x﹚的单调增区间（2）当a＜0且x∈[0,兀／2]时,f﹙x﹚的值域是[3,4]求a,b的值.
f﹙x﹚=a﹙cos²x＋sinxcosx﹚＋b
＝1/2a﹙2cos²x＋2sinxcosx﹚＋b
=1/2a(1+cos2x+sin2x)+b
=√2/2asin(2x+π/4）+1/2a+b
2x+π/4x∈[2kπ-π/2,2kπ+π/2]单调增区间
x∈[kπ-3π/8,kπ+π/8]单调增区间
当a＜0且x∈[0,π／2]时f﹙x﹚的值域是[3,4]
f﹙x﹚=√2/2asin(2x+π/4）+1/2a+b
=√2/2asin[π/2+(2x-π/4)]+1/2a+b
= -√2/2acos(2x-π/4)+1/2a+b
当f﹙0﹚时有最大值＝4
f﹙0﹚=-√2/2acos(-π/4)+1/2a+b=-1/2a1/2a+b=4
b=4
当f﹙[π/2﹚时有最小值＝3
f﹙π/2﹚＝= -√2/2acos(π-π/4)+1/2a+b=3
a+b=3
a=-1
a=-1,b=4
f(x)=1/2*a(2cos²x 1 2sinxcosx-1) b=1/2*a(cos2x sin2x-1) b=1/2*a*√2*sin(2x π/4)-a/2 b
1:sin单调增区间为(-π/2 2kπ,π/2 2kπ)，将(2x π/4)代入上述区间即可求得
2:√2/2*a b-a/2是最大值，b为最小值与值域对应即可求得