求下列函数的最小正周期,递增区间及最大值

求下列函数的最小正周期,递增区间及最大值

（1）y=2sin2xcos2x

（2）y=2cos的平方x/2+1

（3）√3cos4x+sin4x

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2个回答

y = 2 sin2x cos2x

y = sin4x

T = 2π/4 = π/2

ymin = -1 at 4x = 2kπ - π/2

ymax = 1 at 4x = 2kπ + π/2

递增区间[kπ/2 - π/8,kπ/2 + π/8],k∈Z

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y = 2 cos²(x/2) + 1

y = 1 + cosx + 1

y = cosx + 2

T = 2π

ymin = 2 - 1 = 1 at x = 2kπ - π

ymax = 2 + 1 = 3 at x = 2kπ

递增区间[2kπ - π,2kπ],k∈Z

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y = sin4x + √3 cos4x

y = 2 sin(4x + π/3)

T = 2π/4 = π/2

ymin = -2 at 4x + π/3 = 2kπ - π/2,x = kπ/2 - 5π/24

ymax = 2 at 4x + π/3 = 2kπ + π/2,x = kπ/2 + π/24

递增区间[kπ/2 - 5π/24,kπ/2 + π/24],k∈Z

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