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solve for what FOUR values of theta satisfy the following equation: sin(2θ)= -0.8256...

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user7230927 | (Level 1) Salutatorian

Posted May 4, 2013 at 5:17 PM via web

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solve for what FOUR values of theta satisfy the following equation:

sin(2θ)= -0.8256   on   0° < θ < 360°

express answers in degrees to two decimal places.

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted May 4, 2013 at 5:38 PM (Answer #1)

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Solve `sin(2theta)=-0.8256` on `0^@<theta<360^@`

`sin(2theta)=-0.8256`

`2theta=sin^(-1)(0.8256)`

`2theta~~-55.65`

Since we are using `2theta` , to solve for `theta` we can use the reference angle `55.65^@` on the interval `0<2theta<720^@` , with the solutions we seek in the third and fourth quadrants.

`2theta=180+55.65,360-55.65,540+55.65,720-55.65`

To find `theta` we divide each by 2.

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`theta~~117.82^@,152.18^@,297.82^@,332.18^@`

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