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Trigonometry

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Algebra / Geometry / Trigonometry
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Ellipses

Subject: 
Trigonometry
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geometry
Conic sections
Algebraic geometry
Ellipse
Semi-minor axis
Semi-major axis
focus
eccentricity
Circle
Line Segment
Hyperbola
Director circle

An ellipse is the set of points such that the sum of the distances from any point on the ellipse to two other fixed points is constant. The two fixed points are called the foci (plural of focus) of the ellipse. Figure %: The sum of the distances d1 + d2 is the same for any point on the ellipse. The line segment containing the foci of an ellipse with both endpoints on the ellipse is called the major axis. The endpoints of the major axis are called the vertices. The point halfway between the foci is the center of the ellipse. The line segment perpendicular to the major axis and passing through the center, with both endpoints on the ellipse, is the minor axis.

Conics

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Trigonometry
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geometry
Algebraic geometry
Conic sections
Analytic geometry
Curves
Birational geometry
Parabola
Hyperbola
Ellipse
focus
Pole and polar
Euclidean geometry
conics

Analytic geometry is roughly the same as plane geometry except that in analytic geometry, figures are studied in the context of the coordinate plane. Instead of focusing on the congruence of shapes like plane geometry, analytic geometry deals with the coordinates of shapes and formulas for their graphs in the coordinate plane. Much of analytic geometry focuses on the conics. A conic is a two-dimensional figure created by the intersection of a plane and a right circular cone. All conics can be written in terms of the following equation: Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 . The four conics we'll explore in this text are parabolas, ellipses, circles, and hyperbolas.

Trig Identities

Subject: 
Trigonometry
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c? 2012 Math Medics LLC. All rights reserved. TRIGONOMETRIC IDENTITIES ? Reciprocal identities sinu = 1 cscu cosu = 1 secu tanu = 1 cotu cotu = 1 tanu cscu = 1 sinu secu = 1 cosu ? Pythagorean Identities sin2 u+ cos2 u = 1 1 + tan2 u = sec2 u 1 + cot2 u = csc2 u ? Quotient Identities tanu = sinu cosu cotu = cosu sinu ? Co-Function Identities sin( pi 2 ? u) = cosu cos( pi 2 ? u) = sinu tan( pi 2 ? u) = cotu cot( pi 2 ? u) = tanu csc( pi 2 ? u) = secu sec( pi 2 ? u) = cscu ? Parity Identities (Even & Odd) sin(?u) = ? sinu cos(?u) = cosu tan(?u) = ? tanu cot(?u) = ? cotu csc(?u) = ? cscu sec(?u) = secu ? Sum & Difference Formulas sin(u? v) = sinu cos v ? cosu sin v cos(u? v) = cosu cos v ? sinu sin v tan(u? v) = tanu? tan v 1? tanu tan v

Summary of Trig Inverse Function

Subject: 
Trigonometry
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Mathematics
trigonometry
geometry
Mathematical analysis
Inverse trigonometric functions
Sine
Trigonometric functions
Unit Circle
Cartesian coordinate system
Inverse function

Trig Inverse Function Summary Function Meaning Domain Range Quadrants of Found on the (i.e., possible (i.e., possible the Unit Circle calculator by values for x) values for y) from Which Range Values Come j=sin!x y is the angle in the first or [-1, 1] [-nI2, n12] I and IV sin" (X) j=arcsin x fourth quadrant whose sine value is x j=cosir Y is the angle in the first or [-1, 1] [0, n] I and II cos-I(X) y=arccos x second quadrant whose cosine value is x j=tanix y is the angle in the first or (-00, (0) (-nl2, n12) I and IV tan" (X) y=arctanx fourth quadrant whose , tangent value is x

Trig formula sheet

Subject: 
Trigonometry
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Mathematics
Mathematical analysis
Special functions
trigonometry
Analytic functions
logarithms
Exponentials
Natural logarithm
Inverse function
Trigonometric functions
Sine
Inverse trigonometric functions
education

All Rights Reserved: http://regentsprep.org Algebra 2 ? Things to Remember! Exponents: 0 1x ? 1m m x x ? ? ?m n m nx x x ?? ?( )n m n mx x? m m n n x x x ?? n n n x x y y ? ? ?? ?? ? ( ) ?n n nxy x y? Complex Numbers: 1 i? ? ; 0a i a a? ? ? 2 1i ? ? 14 2 1i i? ? ? divide exponent by 4, use remainder, solve. ( ) conjugate ( )a bi a bi? ? 2 2( )( )a bi a bi a b? ? ? ? 2 2a bi a b? ? ? absolute value=magnitude Logarithms log yby x x b? ? ? ln logex x? natural log e = 2.71828? 10log logx x? common log Change of base formula: log log logb a a b

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