Review Sheet _1

Review Sheet _1 - Rev. 2 REVIEW SHEET #1: Trigonometry and...

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Rev. 2 REVIEW SHEET #1: Trigonometry and Vector Algebra Trigonometry: c cos θ = b/c a sin θ = a/c 90 ° θ tan θ = a/b b a 2 + b 2 = c 2 because sin 2 θ + cos 2 θ = 1 How to specify a Vector: A vector has a magnitude and a direction. If a rectangular x, y, z-coordinate system is defined, a vector A r is fully specified in terms of its x-, y-, and z-components; using unit vector notation it is written as k A j A i A A z y x ˆ ˆ ˆ + + = r The magnitude of this vector A r is 2 2 2 x y z A A A A = + + r For such 2-D vectors the magnitude is 2 2 x y A A A = + r and the direction relative to the positive x-axis is atan y x A A θ = . Conversely, if the vector A r has been specified in terms of its magnitude A r and its direction θ (measured counterclockwise from the positive x-axis), the x- and y- components can be found as follows:
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This note was uploaded on 09/11/2011 for the course PHYS 0174 taught by Professor Kohler during the Spring '08 term at Pittsburgh.

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