Question

PENGUIN

f(x)=sin(x+π/3)+2cos(x+π/6) 最大値求め方を教えてください

Answer 1

高橋

sin(x+π/3)=sin(x)cos(π/3)+cos(x)sin(π/3)=(1/2)sin(x)+(√3/2)cos(x)
cos(x+π/6)=cos(x)cos(π/6)-sin(x)sin(π/6)=(√3/2)cos(x)-(1/2)sin(x)
f(x)=(1/2)sin(x)+(√3/2)cos(x)+√3cos(x)-sin(x)=(-1/2)sin(x)+(3√3/2)cos(x)
sinとcosの合成より、f(x)=Asin(x+α)　※A=√((-1/2)²+(3√3/2)²)=√7、α=tan⁻¹((3√3/2)/(-1/2))
-1≦sin(x+α)≦1なので、-√7≦f(x)≦√7