if tan(x)=9/4, find cos(x) if pi<x<3pi/2

Answer 1

pi < x < 3 pi / 2

180 ° < x < 270 °

That is Quadran III

In Quadran III cosine are negative.

cos ( x ) = + OR - 1 /sqrt [ 1 + tan( x ) ^ 2 ]

In this case :

cos ( x ) = - 1 / sqrt [ 1 + tan( x ) ^ 2 ]

cos ( x ) = - 1 / sqrt [ 1 + ( 9 / 4 ) ^ 2 ]

cos ( x ) = - 1 / sqrt ( 1 + 81 / 16 )

cos ( x ) = - 1 / sqrt ( 16 / 16 + 81 / 16 )

cos ( x ) = - 1 / sqrt ( 97 / 16 )

cos ( x ) = - 1 / [ sqrt ( 97 ) / 4 ]

cos ( x ) = - 4 / sqrt ( 97 )

Answer 2

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