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Find the exact value under the given conditions.

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Given sin α = 8/17, with α in quadrant I, and cos β = 3/5

, with β in quadrant I.Find cos (α + β).

asked Oct 31 in PRECALCULUS by anonymous
reshown Nov 1 by bradely

1 Answer

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Given sin α = 8/17 and cos β = 3/5

Cos α  =  √(1 - sin^2 α)

           =  √[ 1 - (8/17)^2 ]

           =  √[ 1 - 64/289 ]

           =  √[ (289 - 64)/289 ]

           =  √[ 225/289 ]

           =  15/17

Sin β  =  [ 1 - cos^2 β ]

          =  [ 1 - (3/5)^2 ]

          =  [ 1 - 9/25 ]

          =  [ (25 - 9)/25 ]

          =  [ 16/25 ]

          =  4/5

Cos (α + β)  =  (Cos α X cos β) - (sin α X sin β)

Substitute corresponding values in Above Equation

Cos (α + β)  =  (15/17)(3/5) - (8/17)(4/5)

                    =  (45/85) - (32/85)

                    =  (45 - 32) / 85

                    =  13 / 85

Answer :

Cos (α + β)  =  13/85.

answered Nov 3 by homeworkhelp Mentor

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