Sumário
- Preface
7The Unit Circle: Sine and Cosine Functions
9Trigonometric Identities and Equations
- Introduction to Trigonometric Identities and Equations
- 9.1Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions
- 9.2Sum and Difference Identities
- 9.3Double-Angle, Half-Angle, and Reduction Formulas
- 9.4Sum-to-Product and Product-to-Sum Formulas
- 9.5Solving Trigonometric Equations
11Systems of Equations and Inequalities
- AProofs, Identities, and Toolkit Functions
- Index
Key Terms
Key Terms
- angle of rotation
- an acute angle formed by a set of axes rotated from the Cartesian plane where, if then is between if then is between and if then
- center of a hyperbola
- the midpoint of both the transverse and conjugate axes of a hyperbola
- center of an ellipse
- the midpoint of both the major and minor axes
- conic section
- any shape resulting from the intersection of a right circular cone with a plane
- conjugate axis
- the axis of a hyperbola that is perpendicular to the transverse axis and has the co-vertices as its endpoints
- degenerate conic sections
- any of the possible shapes formed when a plane intersects a double cone through the apex. Types of degenerate conic sections include a point, a line, and intersecting lines.
- directrix
- a line perpendicular to the axis of symmetry of a parabola; a line such that the ratio of the distance between the points on the conic and the focus to the distance to the directrix is constant
- eccentricity
- the ratio of the distances from a point on the graph to the focus and to the directrix represented by where is a positive real number
- ellipse
- the set of all points in a plane such that the sum of their distances from two fixed points is a constant
- foci
- plural of focus
- focus (of a parabola)
- a fixed point in the interior of a parabola that lies on the axis of symmetry
- focus (of an ellipse)
- one of the two fixed points on the major axis of an ellipse such that the sum of the distances from these points to any point on the ellipse is a constant
- hyperbola
- the set of all points in a plane such that the difference of the distances between and the foci is a positive constant
- latus rectum
- the line segment that passes through the focus of a parabola parallel to the directrix, with endpoints on the parabola
- major axis
- the longer of the two axes of an ellipse
- minor axis
- the shorter of the two axes of an ellipse
- nondegenerate conic section
- a shape formed by the intersection of a plane with a double right cone such that the plane does not pass through the apex; nondegenerate conics include circles, ellipses, hyperbolas, and parabolas
- parabola
- the set of all points in a plane that are the same distance from a fixed line, called the directrix, and a fixed point (the focus) not on the directrix
- polar equation
- an equation of a curve in polar coordinates and
- transverse axis
- the axis of a hyperbola that includes the foci and has the vertices as its endpoints