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What is root x in equation 3cosx+4sinx=0?

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nurli | Honors

Posted July 15, 2013 at 5:32 PM via web

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What is root x in equation 3cosx+4sinx=0?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted July 15, 2013 at 5:55 PM (Answer #1)

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You need to solve for x the equation `3cosx + 4sinx = 0` , hence, you should divide by `cos x` both sides, such that:

`4(sin x/cos x) + 3 = 0/cos x `

Using trigonometric identity `sin x/cos x = tan x` , yields:

`4tan x + 3 = 0 => 4tan x = -3`

`tan x = -3/4 => x = tan^(-1)(-3/4) + n*pi`

`x = -tan^(-1)(3/4) + n*pi`

Hence, evaluating the general solution to the given trigonometric equation, yields ` x = -tan^(-1)(3/4) + n*pi.`

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