Use a half-angle formula to find the exact value of the expression.
$\sin 3 π / 8$

Question

Use a half-angle formula to find the exact value of the expression.  sin  ⁡  3  π      /    8

minotaurafe · Accepted Answer

Let&#039;s say that   θ      /    2  =  3  π      /    8, then this means that   θ  =  3  π      /    4. We shall use the next identity:  sin  ⁡  (      θ    2    )  =  ±                    1        −        cos        ⁡        (        θ        )            2      Where we will use the positive root, given that the angle makes   sin  ⁡  (  θ  ) positive:  sin  ⁡  (            3      π        8    )  =                    1        −        cos        ⁡        (                              3            π                    4                )            2        =                    1        +                  1                      2                              2        =                    1        +                              2                    2                    2        =                              2          +                      2                          2            2        =                    2        +                  2                    4        ≈  0.92388

Use a half-angle formula to find the exact value of theexpression. sin (3pi)/8

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