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20BSP08finalformula

# 20BSP08finalformula - Formula Sheet for Final Exam Trig...

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Unformatted text preview: Formula Sheet for Final Exam Trig identities: sec x = 1 cos x csc x = 1 sin x cot x = cos x sin x cos 2 ( x ) = 1 + cos(2 x ) 2 sin 2 ( x ) = 1 − cos(2 x ) 2 Integrals of trig functions: integraldisplay sec u du = ln | sec u +tan u | + C integraldisplay csc u du = ln | csc u − cot u | + C Average value: Let f be continuous on [ a, b ]. The average value of f on [ a, b ] is f a ve = 1 b − a integraldisplay b a f ( x ) dx. Area under a polar curve: Let R be the region bounded by the polar curve r = f ( θ ) and the rays θ = a and θ = b . Then Area R = integraldisplay b a 1 2 [ f ( θ )] 2 dθ. Complex numbers • n th powers: If z = r (cos θ + i sin θ ), then for any integer n , z n = r n (cos( nθ ) + i sin( nθ )) . • n th roots: For any integer n , the n th roots of r (cos θ + i sin θ ) are r 1 n parenleftbigg cos parenleftbigg θ + k 2 π n parenrightbigg + i sin parenleftbigg θ + k 2 π n parenrightbiggparenrightbigg , k = 0 , 1 . . ., n − 1 ....
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20BSP08finalformula - Formula Sheet for Final Exam Trig...

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