How do you find the exact value of sin ⁡ 105 degrees?

Question

How do you find the exact value of   sin  ⁡  105 degrees?

Clarissa Adkins · Accepted Answer

Use   sin  ⁡  105  =  sin  ⁡  (  60  +  45  )  =  sin  ⁡  60  cos  ⁡  45  +  cos  ⁡  60  sin  ⁡  45  =  (            3        2    )  (      1          2        )  +  (      1    2    )  (      1          2        )  =            2        4    (  (      3    +  1  )  =  0.9656 nearly.Explanation:  sin  ⁡  45  ,  cos  ⁡  45 and   sin  ⁡  60 are irrational.

Talon Mcbride · Accepted Answer

We know   sin  ⁡  (  A  +  B  )  =  sin  ⁡  A  cos  ⁡  B  +  cos  ⁡  A  sin  ⁡  BHence   sin  ⁡      105          ∘        =  sin  ⁡  (      60          ∘        +      45          ∘        )  =  sin  ⁡      60          ∘        cos  ⁡      45          ∘        +  cos  ⁡      60          ∘        sin  ⁡      45          ∘        =            3        2    ×      1          2        +      1    2    ×      1          2        =                    3            +      1              2              2              ×            2              2        =                    6            +              2              4

How do you find the exact value of sin 105 degrees?

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