Trigonometry Flashcards
1.1 Formula of a Radian
1.1: Formula for Arc Length
1.1: Radian and Degree Conversion
1.1: Linear and Angular Speed Formulas
1.1: Area of a Sector of a Circle
1.1: Complementary Angles, Supplementary Angles, Coterminal Angles
Two angles whose sum is 180º.
Two angles whose sum is 90º.
Two angles that share the same initial and terminal sides.
3.1 Law of Sines
3.1: Area of an Oblique Triangle
(two sides and an interior angle)
3.2: Law of Cosines
(three sides, two sides and an interior angle)
3.2: Heron’s Area Formula
(Any triangle, three sides)
3.2: Law of Tangents
(Two sides and an included angle)
3.3: Component form of a Vector
3.3: Magnitude/Length of a Vector
3.3: A Zero Vector and a Unit Vector
3.3: Addition and Scalar Multiplication of Two Vectors
3.3: Finding a Unit Vector
3.3: Angle of a Vector
3.4: Dot Product of Two Vectors
3.4: Finding Magnitude from the Dot Product
3.4: The Angle Between Two Vectors
3.4: Definitions of Orthogonal Vectors
3.4: Projection of u onto v
3.4: Definition of Work
4.1: Complex Conjugate
3.1: Principle Square Root of a Negative Number
4.1: The Fundamental Theorem of Algebra
If f(x) is a polynomial of degree n, where n>0, then f has at least one zero in the complex number system.
4.2: Linear Factorization Theorem
If f(x) is a polynomial of degree n, where n>0, then f has precisely n linear factors.
4.2: The Discriminant
b²–4ac from the quadratic formula.
If b²–4ac<0 the equation has two complex solutions.
If b²–4ac=0 the equation has one repeated real solution.
If b²–4ac>0 the equation has two distinct real solutions.
4.3: Trigonometric Form of a Complex Number
4.3: Multiplication and Division of Two Complex Numbers
4.4: Demoivre’s Theorem
4.4: Finding nth roots of a Complex Number
6.1: Inclination and Slope
6.1: Angle Between Two Lines
6.1: Distance Between a Point and a Line
6.2: Definition of a Parabola
A parabola is the set of all points (x, y) in a plane that are equidistant from a fixed line (directrix) and a fixed point (focus) not on the line.
6.2: Standard Equation of a Parabola
6.2: Focal Chord
A line segment that passes through the focus of a parabola and has endpoints on the parabola.
6.2: Latus Rectum
The specific focal chord perpendicular to the axis of the parabola.
6.2: Finding the Slope Tangent Line at a Point on a Parabola
- Use the distance formula to find the distance between the focus and the point of tangency.
- Subtract the distance found in 1 from the focus in the direction of the axis.
- Use the point slope formula to find the slope of the tangent line.
6.3: Definition of an Ellipse.
An ellipse is the set of all points (x, y)in a plane, the sum of whose distances from two distinct fixed points (foci) is constant.
6.3: Standard Equation of an Ellipse
6.3: Definition of Eccentricity
6.4: Definition of Hyperbola
A hyperbola is the set of all points (x, y)in a plane, the difference of whose distances from two distinct fixed points (foci) is a positive constant.
6.4: Standard Equation of a Hyperbola
6.4: Asymptotes of a Hyperbola
6.5: Equation of Conic in the xy plane.
6.5: Rotation of Axes to Eliminate an xy-Term
6.5: Classification of Conics by the Discriminant
6.6: Definition of a Parametric Equation
Writing both x and y as functions of a third variable.
6.6: Definition of Plane Curve
If f and g are continuous functions of t on the interval I, the set of ordered pairs (f (t )), (g (t )) is a plane curve C.
6.6: Eliminating the Parameter
Converting Parametric Equations into a Rectangular Equation
- Parametric Equations
- Solve for the parametric variable in one equation
- Substitute in the other equation
- Rectangular Equation
6.7: Polar Coordinate System
6.7: Coordinate Conversion
6.7: Equation Conversion
P.2: The Quadratic Formula
P.3: The Distance Formula
P.3: The Midpoint Formula
P.3: Standard Form of the Equation of a Circle
P:4: The Slope of a Line Passing Through Two Points
P.4: Point-Slope Form of the Equation of a Line
1.5: Graphs of Sine and Cosine Functions
Define each parameter
2.1: Reciprocal Identities of the 6 Trigonometric Functions
2.1: Quotient Identities of Tangent and Cotangent
2.1: Pythagorean Identities
2.1: 6 Trigonometric Cofunction Identities
2.1: Even/Odd Identities of 6 Trigonometric Functions
2.4: Sum and Difference Formulas (sin)
2.4: Sum and Difference Formulas
2.4: Sum and Difference Formulas
2.5: Double-Angle Formulas (sin)
2.5: Double-Angle Formulas (cos)
2.5: Double-Angle Formulas (tan)
2.5: Power-Reducing Formulas (sin)
2.5: Power-Reducing Formulas (cos)
2.5: Power-Reducing Formulas (tan)
2.5: Product-to-Sum Formulas
2.5: Product-to-Sum Formulas
2.5: Product-to-Sum Formulas
2.5: Product-to-Sum Formulas
2.5: Sum-to-Product Formulas
2.5: Sum-to-Product Formulas
2.5: Sum-to-Product Formulas
2.5: Sum-to-Product Formulas
5.1: Formulas for Compound Interest
5.3: Logorithm Change-of-Base Formulas
5.5: Exponential Growth Model
5.5: Exponential Decay Model
5.5: Gaussian Model
5.5: Logistic Growth Model
5.5: Logarithmic Models
