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

Emmy Swanson 2022-10-25 Answered
Rewrite sin ( x + 7 π 6 ) in terms of sin(x) and cos(x)
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Answers (1)

Aidyn Mccarthy
Answered 2022-10-26 Author has 12 answers
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 ) ]
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