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How to solve the equation square root 3*sin x-cosx=0?

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doorsreb | Student, Grade 11 | eNoter

Posted June 8, 2011 at 11:41 PM via web

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How to solve the equation square root 3*sin x-cosx=0?

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giorgiana1976 | College Teacher | Valedictorian

Posted June 8, 2011 at 11:44 PM (Answer #1)

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First, we'll shift cos x to the right side:

sqrt3*sin x = cos x

We'll divide by cos x both sides:

sqrt3*sin x/cos x = 1

But the fraction sin x/cos x can be replaced by the tangent function tan x.

sqrt3*tan x = 1

tan x = 1/sqrt3

Since it is not allowed to keep the square root to denominator, we'll multiply both, numerator and denominator, by sqrt3.

tan x = sqrt3/3

x = arctan (sqrt3/3) + k*pi

x = pi/6 + k*pi

The set of solutions of the equation is: {pi/6 + k*pi}.

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chrisbond437 | Student , Grade 10 | Honors

Posted June 16, 2011 at 8:43 PM (Answer #2)

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sin x/cos x=1/sqrt(3)

tan x=1/sqrt 3

we know tan 30=1/sqrt 3

»x=30

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