formulaF_F08

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

This preview shows pages 1–2. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online