函数y=3arccos(sinx),x∈[2kπ-π/4,2kπ+5π/6](k∈z的值域)
问题描述:
函数y=3arccos(sinx),x∈[2kπ-π/4,2kπ+5π/6](k∈z的值域)
答
y=3arccos(sinx),x∈[2kπ-π/4,2kπ+5π/6](k∈z的值域)
y/3=arccos(sinx)=α,0≤α≤π
cosα=sinx
x∈[2kπ-π/4,2kπ+5π/6](k∈z)
-√2/2≤sinx≤1
-√2/2≤cosα≤1
0≤α≤3π/4
0≤y≤9π/4