# mathematics

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find the maximum value of √3 cosθ-sinθ.???

• mathematics -

You get a maximum when the derivative is zero.

-ã3 sin ƒÆ -cos ƒÆ = 0
tan ƒÆ = -1/ã3

ƒÆ = -30 degrees

ã3 cosƒÆ-sinƒÆ = 3/2 + 1/2 = 2

check: If theta = -29 degrees,
ã3 cosƒÆ-sinƒÆ = 1.5149 + 0.4848 = 1.9997
If theta = -31 degrees,
ã3 cosƒÆ-sinƒÆ = 1.4847 + 0.5150 = 1.9997
So it looks like the maximum is 2.

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