Rewrite sin ⁡ ( x + 7 π 6 ) in terms of sin(x) and cos(x)

Question

Rewrite   sin  ⁡  (  x  +            7      π        6    ) in terms of sin(x) and cos(x)

Aidyn Mccarthy · Accepted Answer

Solution:It is asked to write   sin  ⁡  (  x  +            7      Π        6    ) in terms of sin(x) and cos(x).Using the identity,  sin  ⁡  (  a  +  b  )  =  sin  ⁡  (  a  )  cos  ⁡  (  b  )  +  cos  ⁡  (  a  )  sin  ⁡  (  b  )  ,Where  a  =  x    b  =            7      Π        6      sin  ⁡  (  x  +            7      Π        6    )  =  sin  ⁡  (  x  )  cos  ⁡  (            7      Π        6    )  +  cos  ⁡  (  x  )  sin  ⁡  (            7      Π        6    )    sin  ⁡  (            7      Π        6    )  =  sin  ⁡  (  Π  +      Π    6    )Using identity   sin  ⁡  (  Π  +  Θ  )  =  −  sin  ⁡  (  Θ  )    sin  ⁡  (            7      Π        6    )  =  −  sin  ⁡  (      Π    6    )    sin  ⁡  (            7      Π        6    )  =  −      1    2      cos  ⁡  (            7      Π        6    )  =  cos  ⁡  (  Π  +      Π    6    )Using identity   cos  ⁡  (  Π  +  Θ  )  =  −  cos  ⁡  (  Θ  )    cos  ⁡  (            7      Π        6    )  =  −  cos  ⁡  (      Π    6    )    cos  ⁡  (            7      Π        6    )  =  −            3        2  Our expression becomes  sin  ⁡  (  x  +            7      Π        6    )  =  sin  ⁡  (  x  )  (  −            3        2    )  +  cos  ⁡  (  x  )  (  −      1    2    )    sin  ⁡  (  x  +            7      Π        6    )  =  −            3        2    sin  ⁡  (  x  )  −      1    2    cos  ⁡  (  x  )    sin  ⁡  (  x  +            7      Π        6    )  =  −      1    2        [          3        sin    ⁡    (    x    )    +    cos    ⁡    (    x    )    ]

Rewrite sin(x+7pi/6) in terms of sin(x) and cos(x)

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