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Solve the following equation for  `0^olt=xlt360^o` . `sin^2x=1/2` What is the answer...

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lkballer24 | Student, Grade 11 | Valedictorian

Posted August 18, 2013 at 11:11 PM via web

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Solve the following equation for  `0^olt=xlt360^o` .

`sin^2x=1/2`

What is the answer for question 1) ?

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Mary Joy Ripalda | High School Teacher | (Level 3) Educator

Posted August 19, 2013 at 12:11 AM (Answer #1)

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`sin^2x=1/2`

To solve for x, take the square root of both sides of the equation.

`sqrt(sin^2x)=+-sqrt(1/2)`

`sinx=+-sqrt1/sqrt2`

`sinx=+-1/sqrt2`

Then, rationalize the denominator.

`sinx=+-1/sqrt2*sqrt2/sqrt2`

`sinx=+-sqrt2/2`

And take the inverse sine to to have x only on the left side of the equation.

`x=sin^(-1)(+-sqrt2/2)`

Hence, `x=45^o, 135^o, 225^o and 315^o` .

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