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Use the angle sum identities to find the exact value of trigonometric expression. Show...

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Use the angle sum identities to find the exact value of trigonometric expression. Show all work

Sin255 Degrees

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jeew-m's profile pic

Posted (Answer #1)

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we know that;

`sin(180+theta) = -sintheta`

 

`sin(255) = sin(180+75) = -sin75`

 

`sin75 = sin(45+30)`

We know that;

`sin(A+B) = sinAcosB+cosAsinB`

 

`sin75 `

`= sin(45+30)`

`= sin45xxcos30+cos45xxsin30`

`= (1/sqrt2xxsqrt3/2+1/sqrt2xx1/2)`

`= (sqrt3+1)/(2sqrt2)`

 

So finally the answer is;

`sin(255) = sin(180+75) = -sin75 = -(sqrt3+1)/(2sqrt2) = 9659`

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