formulaF_F08 - Sec 01-06 Calculus 251 Formula Sheet FALL...

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Sec 01-06 Calculus 251 Formula Sheet FALL 2008 Trig: sin 2 x + cos 2 x = 1 sec 2 x = 1 + tan 2 x sin 2 x = 1 - cos 2 x 2 cos 2 x = 1 + cos 2 x 2 Angle x: 0 , 2 π π 6 π 4 π 3 π 2 2 π 3 3 π 4 5 π 6 π 3 π 2 sin x :0 1 2 2 2 3 2 1 3 2 2 2 1 2 0 - 1 cos x :1 3 2 2 2 1 2 0 - 1 2 - 2 2 - 3 2 - 10 tan x 3 3 1 3 undef - 3 - 1 - 3 3 0 undef Line: x = x o + at y = y o + bt z = z o + ct where the direction vector is ± a,b,c ² Plane: a ( x - x o )+ b ( y - y o c ( z - z o ) = 0 where n = ± ² Quadric Surfaces: * note: if a = b = c , then the ellipsoid is a sphere. Ellipsoid: * x 2 a 2 + y 2 b 2 + z 2 c 2 = 1 Hyperboloid of One Sheet: x 2 a 2 + y 2 b 2 - z 2 c 2 =1 Hyperboloid of Two Sheets: - x 2 a 2 - y 2 b 2 + z 2 c 2 = 1 Cone: x 2 a 2 + y 2 b 2 = z 2 c 2 Elliptic Paraboloid: x 2 a 2 + y 2 b 2 = z c Hyperbolic Paraboloid: x 2 a 2 - y 2 b 2 = z c Coordinate Conversion: From Cylindrical to Rectangular: x = r cos θy = r sin θz = z From Rectangular to Cylindrical: r 2 = x 2 + y 2 tan θ = y x z = z From Spherical to Rectangular: x = ρ sin φ cos = ρ sin φ sin = ρ cos φ
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formulaF_F08 - Sec 01-06 Calculus 251 Formula Sheet FALL...

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