If your question mean:
Determine an exact value for sin ( x + y )
then:
sin ( x + y ) = sin x ∙ cos y + cos x ∙ sin y
sin x = 4 / 5
cos x = ± √ ( 1 - sin² x )
In the first quadrant, all trigonometric functions are positive, so:
cos x = √ ( 1 - sin² x )
cos x = √ [ 1 - ( 4 / 5 )² ]
cos x = √ ( 1 - 16 / 25 )
cos x = √ ( 25 / 25 - 16 / 25 )
cos x = √ ( 9 / 25 )
cos x = √ 9 / √ 25
cos x = 3 / 5
cos y = 7 / 25
sin y = ± √ ( 1 - cos² y )
In the first quadrant, all trigonometric functions are positive, so:
sin y = √ ( 1 - cos² y )
sin y = √ [ 1 - ( 7 / 25 )² y )
sin y = √ ( 1 - 49 / 625 )
sin y = √ ( 625 / 625 - 49 / 625 )
sin y = √ ( 576 / 625 )
sin y = √ 576 / √ 625
sin y = 24 / 25
sin ( x + y ) = sin x ∙ cos y + cos x ∙ sin y
sin ( x + y ) = 4 / 5 ∙ 7 / 25 + 3 / 5 ∙ 24 / 25
sin ( x + y ) = 28 / 125 + 72 / 125
sin ( x + y ) = 100 / 125
sin ( x + y ) = 25 ∙ 4 / 25 ∙ 5
sin ( x + y ) = 4 / 5
Angles x and y are located in the first quadrant such that sinx= 4/5 and cosy= 7/25.
determine an exact value for xin(x+Y)
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