COSMOS Chapter 3 Solution 36 | Answer Key - Edubirdie

University:
Michigan State University
Course:
ERG 160 | Success in Science, Technology, Engineering, and Mathematics
Academic year:

2024
Views:

50

Pages:

1
Author:

Lily Callahan

COSMOS: Complete Online Solutions Manual Organization System Chapter 3, Solution 36. By definition B ⋅ C = BC cos (α − β ) where B = B ( cos β ) i + ( sin β ) j C = C ( cos α ) i + ( sin α ) j ∴ ( B cos β )( C cos α ) + ( B sin β )( C sin α ) = BC cos (α − β ) cos β cos α + sin β sin α = cos (α − β ) or (1) By definition B′⋅ C = BC cos (α + β ) where B′ = ( cos β ) i − ( sin β ) j ∴ ( B cos β )( C cos α ) + ( − B sin β )( C sin α ) = BC cos (α + β ) or cos β cos α − sin β sin α = cos (α + β ) (2) Adding Equations (1) and (2), 2 cos β cos α = cos (α − β ) + cos (α + β ) or cos α cos β = . 1 1 cos (α + β ) + cos (α − β ) W 2 2

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