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Trigonometry > Trigonometry > Flashcards

Trigonometry Flashcards

1
Q

1.1 Formula of a Radian

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2
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1.1: Formula for Arc Length

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3
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1.1: Radian and Degree Conversion

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4
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1.1: Linear and Angular Speed Formulas

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5
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1.1: Area of a Sector of a Circle

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6
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1.1: Complementary Angles, Supplementary Angles, Coterminal Angles

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Two angles whose sum is 180º.

Two angles whose sum is 90º.

Two angles that share the same initial and terminal sides.

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7
Q

3.1 Law of Sines

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8
Q

3.1: Area of an Oblique Triangle

(two sides and an interior angle)

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9
Q

3.2: Law of Cosines

(three sides, two sides and an interior angle)

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10
Q

3.2: Heron’s Area Formula

(Any triangle, three sides)

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11
Q

3.2: Law of Tangents

(Two sides and an included angle)

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12
Q

3.3: Component form of a Vector

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13
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3.3: Magnitude/Length of a Vector

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14
Q

3.3: A Zero Vector and a Unit Vector

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15
Q

3.3: Addition and Scalar Multiplication of Two Vectors

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16
Q

3.3: Finding a Unit Vector

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17
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3.3: Angle of a Vector

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18
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3.4: Dot Product of Two Vectors

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19
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3.4: Finding Magnitude from the Dot Product

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20
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3.4: The Angle Between Two Vectors

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21
Q

3.4: Definitions of Orthogonal Vectors

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22
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3.4: Projection of u onto v

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23
Q

3.4: Definition of Work

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24
Q

4.1: Complex Conjugate

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25
Q

3.1: Principle Square Root of a Negative Number

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26
Q

4.1: The Fundamental Theorem of Algebra

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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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27
Q

4.2: Linear Factorization Theorem

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If f(x) is a polynomial of degree n, where n>0, then f has precisely n linear factors.

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28
Q

4.2: The Discriminant

A

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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29
Q

4.3: Trigonometric Form of a Complex Number

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30
Q

4.3: Multiplication and Division of Two Complex Numbers

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31
Q

4.4: Demoivre’s Theorem

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32
Q

4.4: Finding nth roots of a Complex Number

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33
Q

6.1: Inclination and Slope

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34
Q

6.1: Angle Between Two Lines

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35
Q

6.1: Distance Between a Point and a Line

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36
Q

6.2: Definition of a Parabola

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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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37
Q

6.2: Standard Equation of a Parabola

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38
Q

6.2: Focal Chord

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A line segment that passes through the focus of a parabola and has endpoints on the parabola.

39
Q

6.2: Latus Rectum

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The specific focal chord perpendicular to the axis of the parabola.

40
Q

6.2: Finding the Slope Tangent Line at a Point on a Parabola

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  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.
41
Q

6.3: Definition of an Ellipse.

A

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.

42
Q

6.3: Standard Equation of an Ellipse

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43
Q

6.3: Definition of Eccentricity

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44
Q

6.4: Definition of Hyperbola

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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.

45
Q

6.4: Standard Equation of a Hyperbola

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46
Q

6.4: Asymptotes of a Hyperbola

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47
Q

6.5: Equation of Conic in the xy plane.

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48
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6.5: Rotation of Axes to Eliminate an xy-Term

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49
Q

6.5: Classification of Conics by the Discriminant

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50
Q

6.6: Definition of a Parametric Equation

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Writing both x and y as functions of a third variable.

51
Q

6.6: Definition of Plane Curve

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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.

52
Q

6.6: Eliminating the Parameter

Converting Parametric Equations into a Rectangular Equation

A
  1. Parametric Equations
  2. Solve for the parametric variable in one equation
  3. Substitute in the other equation
  4. Rectangular Equation
53
Q

6.7: Polar Coordinate System

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​

54
Q

6.7: Coordinate Conversion

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55
Q

6.7: Equation Conversion

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56
Q

P.2: The Quadratic Formula

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57
Q

P.3: The Distance Formula

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58
Q

P.3: The Midpoint Formula

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59
Q

P.3: Standard Form of the Equation of a Circle

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60
Q

P:4: The Slope of a Line Passing Through Two Points

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61
Q

P.4: Point-Slope Form of the Equation of a Line

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62
Q

1.5: Graphs of Sine and Cosine Functions

Define each parameter

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63
Q

2.1: Reciprocal Identities of the 6 Trigonometric Functions

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64
Q

2.1: Quotient Identities of Tangent and Cotangent

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65
Q

2.1: Pythagorean Identities

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66
Q

2.1: 6 Trigonometric Cofunction Identities

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67
Q

2.1: Even/Odd Identities of 6 Trigonometric Functions

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68
Q

2.4: Sum and Difference Formulas (sin)

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69
Q

2.4: Sum and Difference Formulas

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70
Q

2.4: Sum and Difference Formulas

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71
Q

2.5: Double-Angle Formulas (sin)

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72
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2.5: Double-Angle Formulas (cos)

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73
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2.5: Double-Angle Formulas (tan)

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74
Q

2.5: Power-Reducing Formulas (sin)

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75
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2.5: Power-Reducing Formulas (cos)

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76
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2.5: Power-Reducing Formulas (tan)

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77
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2.5: Product-to-Sum Formulas

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78
Q

2.5: Product-to-Sum Formulas

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79
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2.5: Product-to-Sum Formulas

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80
Q

2.5: Product-to-Sum Formulas

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81
Q

2.5: Sum-to-Product Formulas

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82
Q

2.5: Sum-to-Product Formulas

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83
Q

2.5: Sum-to-Product Formulas

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84
Q

2.5: Sum-to-Product Formulas

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85
Q

5.1: Formulas for Compound Interest

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86
Q

5.3: Logorithm Change-of-Base Formulas

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87
Q

5.5: Exponential Growth Model

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88
Q

5.5: Exponential Decay Model

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89
Q

5.5: Gaussian Model

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90
Q

5.5: Logistic Growth Model

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91
Q

5.5: Logarithmic Models

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Trigonometry (1 decks)

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