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Given tang `theta/2` =1/`sqrt3` , what is sin `theta` ?

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minlux | Honors

Posted July 25, 2013 at 4:42 PM via web

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Given tang `theta/2` =1/`sqrt3` , what is sin `theta` ?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted July 25, 2013 at 5:01 PM (Answer #1)

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You should use the following trigonometric identity that helps you to evaluate `sin theta` in terms of `tan (theta/2)` , such that:

`sin theta = (2 tan(theta/2))/(1 + tan^2(theta/2))`

Since the problem provides the value of `tan(theta/2)` , you need to replace `1/sqrt3` for `tan(theta/2)` in equation above, such that:

`sin theta = (2/sqrt3)/(1 + 1/3) => sin theta = (2/sqrt3)/(4/3)`

Reducing duplicate factors yields:

`sin theta = (1/sqrt3)/(2/(sqrt 3*sqrt 3)) => sin theta = 1/(2/sqrt 3)`

`sin theta = sqrt3/2`

Hence, evaluating `sin theta` , under the given conditions, yields `sin theta = sqrt3/2` .

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