f(x)=a(sinx×sinx+cosx×sinx),当x属于[-3/8π,1/4π]时有最大值1/2,求a

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f(x)=a(sinx×sinx+cosx×sinx),当x属于[-3/8π,1/4π]时有最大值1/2,求a
f(x)=a(sinx×sinx+cosx×sinx),当x属于[-3/8π,1/4π]时有最大值1/2,求a

f(x)=a(sinx×sinx+cosx×sinx),当x属于[-3/8π,1/4π]时有最大值1/2,求a
f(x)=a( (sinx) ^2 +cosxsinx)
=a(1/2 - (cos2x) /2 + (sin2x) /2 )
=a/2+(a/2)*(sin2x -cos2x)
=a/2 + (a/2)*√2 * sin(2x-π/4)
x∈[-3/8π,1/4π]
2x-π/4∈[-π,π/4]
sin(2x-π/4)≤(√2)/2
f(x)≤a/2 +(a/2)*√2*(√2)/2=a=1/2
∴a=1/2