Find the solution of sinx=-(sqrt(3))/2....

Find the solution of `sinx=-(sqrt(3))/2`.

Text Solution

Verified by Experts

The correct Answer is:

`x = n pi + (-1)^n ((4 pi)/3), n in mathbbZ`

`sinx=-(sqrt(3))/2`
`=-sin(pi/3)`
`=sin(pi + pi/3)`
`=sin((4 pi)/3)`
`implies x = n pi + (-1)^n ((4 pi)/3), \ \ n in mathbbZ`

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Knowledge Check

The principal solution of sinx=-(sqrt(3))/(2) is

A

`(pi)/(3)`

B

`(4pi)/(3)`

C

`(2pi)/(3)`

D

`-(4pi)/(3)`

General solution of sinx=(sqrt(3))/(2) is

A

`npi+(-1)^(n)(pi)/(3), ninZ`

B

`2npi+(-1)^(n)(pi)/(3), ninZ`

C

`npi+(-1)^(n-1)(pi)/(3), ninZ`

D

`npi+(-1)^(n+1)(pi)/(3), ninZ`

General solution of sinx=(-sqrt(3))/(2) is

A

`npi+(-1)^(n)(pi)/(3), ninZ`

B

`npi+(-1)^(n)(5pi)/(3), ninZ`

C

`npi+(-1)^(n)(7pi)/(3), ninZ`

D

`npi+(-1)^(n)(4pi)/(3), ninZ`

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The principal solution of sinx=(-1)/(sqrt(2)) is

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