函数y=cos(x+5°)+3√2 cos(x+50°)的值域是?

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函数y=cos(x+5°)+3√2cos(x+50°)的值域是?函数y=cos(x+5°)+3√2cos(x+50°)的值域是?函数y=cos(x+5°)+3√2cos(x+50°)的值域是?y=co

函数y=cos(x+5°)+3√2 cos(x+50°)的值域是?
函数y=cos(x+5°)+3√2 cos(x+50°)的值域是?

函数y=cos(x+5°)+3√2 cos(x+50°)的值域是?
y=cos(x+5°)+3√2 cos(x+50°)
=cos(x+5°)+3√2 cos(x+5°+45°)
=cos(x+5°)+3√2 [cos(x+5°)cos45°-sin(x+5°)sin45°]
=cos(x+5°)+3 [cos(x+5°)-sin(x+5°)]
=4cos(x+5°)-3sin(x+5°)
=5[4/5*cos(x+5°)-3/5*sin(x+5°)]
=5cos[x+π/36+arccos(4/5)]
故值域为[-5,5]