cosX+sinX+1的值域和单调区间是多少?
1个回答

你想说的公式是asinx+bcosx=√(a²+b²)sin(x+φ) 其中sinφ=b/a,

cosx+sinx+1

=√2sin(x+π/4)+1

-1≤sin(x+π/4)≤1

1-√2≤√2sin(x+π/4)+1≤√2+1

函数的值域为[1-√2,√2+1]

2kπ-π/2≤x+π/4≤2kπ+π/2 (k∈Z)时,即2kπ-3π/4≤x≤2kπ+π/4 (k∈Z),函数单调递增.

2kπ+π/2≤x+π/4≤2kπ+3π/2 (k∈Z)时,即2kπ+π/4≤x≤2kπ+5π/4 (k∈Z),函数单调递减.

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