Lecture 7 Notes

Ie cos2asin2a 1 applications vibrations 37

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Unformatted text preview: cos(A) sin(B ) cos(A + B ) = cos(A) cos(B ) − sin(A) sin(B ) 2 cos(3t + π /3) = 2 cos(π /3) cos(3t) − 2 sin(π /3) sin(3t) = cos(3t) − √ 3 sin(3t) Applications - vibrations (3.7) • Converting from sum-of-sin-cos to a single cos expression: • Example: 4 cos(2t) + 3 sin(2t) cos(A − B ) = cos(A) cos(B ) + sin(A) sin(B ) Applications - vibrations (3.7) • Converting from sum-of-sin-cos to a single cos expression: • Example: 4 cos(2t) + 3 sin(2t) 4 3 cos(A − B ) = cos(A) cos(B ) + sin(A) sin(B ) Applications - vibrations (3.7) • Converting from sum-of-sin-cos to a single cos expression: • Example: 4 cos(2t) + 3 sin(2t) 4 3 cos(A − B ) = cos(A) cos(B ) + sin(A) sin(B ) (cos(A), sin(A)) must lie on the unit circle. i.e. cos2(A)+sin2(A) = 1. Applications - vibrations (3.7) • Converting from sum-of-sin-cos to a single cos expression: • Example: 4 cos(2t) + 3 sin(2t) ￿ ￿ 4 3 =5 cos(2t) + sin(2t) 5 5 4 3 cos(A − B ) = cos(A) cos(B ) + sin(A) sin(B ) (cos(A), sin(A)) must lie on t...
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