Trigonometry Flashcards
1
Q
1.1 Formula of a Radian
A
2
Q
1.1: Formula for Arc Length
A
3
Q
1.1: Radian and Degree Conversion
A
4
Q
1.1: Linear and Angular Speed Formulas
A
5
Q
1.1: Area of a Sector of a Circle
A
6
Q
1.1: Complementary Angles, Supplementary Angles, Coterminal Angles
A
Two angles whose sum is 180º.
Two angles whose sum is 90º.
Two angles that share the same initial and terminal sides.
7
Q
3.1 Law of Sines
A
8
Q
3.1: Area of an Oblique Triangle
(two sides and an interior angle)
A
9
Q
3.2: Law of Cosines
(three sides, two sides and an interior angle)
A
10
Q
3.2: Heron’s Area Formula
(Any triangle, three sides)
A
11
Q
3.2: Law of Tangents
(Two sides and an included angle)
A
12
Q
3.3: Component form of a Vector
A
13
Q
3.3: Magnitude/Length of a Vector
A
14
Q
3.3: A Zero Vector and a Unit Vector
A
15
Q
3.3: Addition and Scalar Multiplication of Two Vectors
A
16
Q
3.3: Finding a Unit Vector
A
17
Q
3.3: Angle of a Vector
A
18
Q
3.4: Dot Product of Two Vectors
A
19
Q
3.4: Finding Magnitude from the Dot Product
A
20
Q
3.4: The Angle Between Two Vectors
A
21
Q
3.4: Definitions of Orthogonal Vectors
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22
Q
3.4: Projection of u onto v
A
23
Q
3.4: Definition of Work
A
24
Q
4.1: Complex Conjugate
A
25
3.1: Principle Square Root of a Negative Number
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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.
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4.2: Linear Factorization Theorem
If f(x) is a polynomial of degree n, where n\>0, then f has precisely n linear factors.
28
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.
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4.3: Trigonometric Form of a Complex Number
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4.3: Multiplication and Division of Two Complex Numbers
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4.4: Demoivre's Theorem
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4.4: Finding nth roots of a Complex Number
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6.1: Inclination and Slope
34
6.1: Angle Between Two Lines
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6.1: Distance Between a Point and a Line
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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.
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6.2: Standard Equation of a Parabola
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6.2: Focal Chord
A line segment that passes through the focus of a parabola and has endpoints on the parabola.
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6.2: Latus Rectum
The specific focal chord perpendicular to the axis of the parabola.
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6.2: Finding the Slope Tangent Line at a Point on a Parabola
1. Use the distance formula to find the distance between the focus and the point of tangency.
2. Subtract the distance found in 1 from the focus in the direction of the axis.
3. Use the point slope formula to find the slope of the tangent line.
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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.
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6.3: Standard Equation of an Ellipse
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6.3: Definition of Eccentricity
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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.
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6.4: Standard Equation of a Hyperbola
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6.4: Asymptotes of a Hyperbola
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6.5: Equation of Conic in the *xy* plane.
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6.5: Rotation of Axes to Eliminate an xy-Term
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6.5: Classification of Conics by the Discriminant
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6.6: Definition of a Parametric Equation
Writing both *x* and *y* as functions of a third variable.
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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.*
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6.6: Eliminating the Parameter
Converting Parametric Equations into a Rectangular Equation
1. Parametric Equations
2. Solve for the parametric variable in one equation
3. Substitute in the other equation
4. Rectangular Equation
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6.7: Polar Coordinate System
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6.7: Coordinate Conversion
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6.7: Equation Conversion
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P.2: The Quadratic Formula
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P.3: The Distance Formula
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P.3: The Midpoint Formula
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P.3: Standard Form of the Equation of a Circle
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P:4: The Slope of a Line Passing Through Two Points
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P.4: Point-Slope Form of the Equation of a Line
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1.5: Graphs of Sine and Cosine Functions
Define each parameter
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2.1: Reciprocal Identities of the 6 Trigonometric Functions
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2.1: Quotient Identities of Tangent and Cotangent
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2.1: Pythagorean Identities
66
2.1: 6 Trigonometric Cofunction Identities
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2.1: Even/Odd Identities of 6 Trigonometric Functions
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2.4: Sum and Difference Formulas (sin)
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2.4: Sum and Difference Formulas
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2.4: Sum and Difference Formulas
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2.5: Double-Angle Formulas (sin)
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2.5: Double-Angle Formulas (cos)
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2.5: Double-Angle Formulas (tan)
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2.5: Power-Reducing Formulas (sin)
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2.5: Power-Reducing Formulas (cos)
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2.5: Power-Reducing Formulas (tan)
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2.5: Product-to-Sum Formulas
78
2.5: Product-to-Sum Formulas
79
2.5: Product-to-Sum Formulas
80
2.5: Product-to-Sum Formulas
81
2.5: Sum-to-Product Formulas
82
2.5: Sum-to-Product Formulas
83
2.5: Sum-to-Product Formulas
84
2.5: Sum-to-Product Formulas
85
5.1: Formulas for Compound Interest
86
5.3: Logorithm Change-of-Base Formulas
87
5.5: Exponential Growth Model
88
5.5: Exponential Decay Model
89
5.5: Gaussian Model
90
5.5: Logistic Growth Model
91
5.5: Logarithmic Models
