Question

当x∈[π/6,7π/6]时，函数y=3-sinx-2cos²x的值域为

Answer 1

y=3-sinx-2cos²x
=2（sinx-1/4）²+7/8
当x∈[π/6,7π/6]时，函数y=3-sinx-2cos²x的值域为[7/8，2]

Answer 2

y=3-sinx-2cos²x
=2sin²x-sinx+1
=2(sinx-1/4)²+7/8

因 x∈[π/6, 7π/6]
故 sinx∈[-1/2, 1]

故 (sinx-1/4)²∈[0, 9/16]
故 y∈[7/8, 2]