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formulas_sheetw

# formulas_sheetw - You may find some of the following...

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You may find some of the following formulas useful (but probably not all of them) sin 2 ( x ) + cos 2 ( x ) = 1 and cos(2 x ) = cos 2 ( x ) - sin 2 ( x ) sin(2 x ) = 2 sin( x ) cos( x ) and sin 2 ( x ) = 1 - cos(2 x ) 2 cos 2 ( x ) = 1 + cos(2 x ) 2 cos( π/ 3) = 1 / 2 and sin( π/ 3) = 3 / 2. cos( π/ 4) = 2 / 2 and sin( π/ 4) = 2 / 2. cos( π/ 6) = 3 / 2 and sin( π/ 6) = 1 / 2. cos(0) = 1 and sin(0) = 0. d dx csc( x ) = - csc( x ) cot( x ) . d dt sec( t ) = sec( t ) tan( t ) . d tan( θ ) = sec 2 ( θ ) . d dr cot( r ) = - csc 2 ( r ) . Arc length function: Length of curve from ( x ( α ) , y ( α ) , z ( α )) to ( x ( t ) , y ( t ) , z ( t )) is s ( t ) = R t α | r 0 ( u ) | du. T ( t ) = r 0 ( t ) | r 0 ( t ) | , N ( t ) = T 0 ( t ) | T 0 ( t ) | , B ( t ) = T ( t ) × N ( t ) . proj b a = b · a | b | 2 b , comp b a = b · a | b | • h a, b, c i × h d, e, f
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