Integrating Parametric Equations: Summary

Trigonometric Formulae

1. Introduction to Trigonometric Formulae
2. The Sine Rule
3. Using the Sine rule to calculate unknown side lengths
4. Using the Sine rule to calculate unknown angles
5. When the Sine Rule Identifies Two Possible Angles
6. When the Sine Rule Identifies Two Possible Angles
7. Why does subtracting from 180 give us the size of obtuse angles?
8. T
9. he Cosine Rule
10. Using the Cosine Rule to calculate unknown angles
11. Choosing between Soh Cah Toa, Sine Rule and Cosine Rule
12. Finding Triangle Area Using the Sine Function

The Unit Circle

1. Introduction to the Unit Circle
2. Sine and Cosine’s First Outputs – Part 1
3. Sine and Cosine’s First Outputs – Part 2
4. Tangent’s First Outputs
5. Where Does Sine Get Its Name From?
6. All the Other Outputs For Sine – Part 1
7. All the Other Outputs For Sine – Part 2
8. All the Other Outputs For Cosine
9. All the Other Outputs For Tangent
10. Negative Outputs from the Tangent Function
11. Why is the Output from Tangent Opposite over Adjacent? – Part 1
12. Why is the Output from Tangent Opposite over Adjacent? – Part 2
13. The First Trigonometric Identities

Solving Trigonometric Equations

1. Solving Trigonometric Equations – Introduction
2. Substituting Trig Functions – Part 1
3. The CAST Diagram
4. Substituting Trig Functions – Part 2
5. Acute Angles and The Sine Function – Part 1
6. Acute Angles and The Sine Function – Part 2
7. Acute Angles and The Sine Function – Part 3
8. Acute Angles and the Cosine Function
9. Acute Angles and the Tangent Function
10. Solving Linear Equations with Trigonometric Functions – Part 1
11. Solving Linear Equations with Trigonometric Functions – Part 2
12. Solving Linear Equations with Trigonometric Functions – Part 3
13. Solving Trig Equations Using the Tan Identity – Part 1
14. Solving Trig Equations Using the Tan Identity – Part 2
15. Solving Trig Equations Using the Tan Identity – Part 3
16. When the Tan Identity Can’t Be Used
17. Solving Trig Equations Using the Pythagorean Identity – Part 1
18. Solving Trig Equations Using the Pythagorean Identity – Part 2
19. Solving Trig Equations When the Input Isn’t Theta – Part 1
20. Solving Trig Equations When the Input Isn’t Theta – Part 2
21. Solving Trig Equations When the Input Isn’t Theta – Part 3
22. Recognising quadratic equations with trigonometric functions – Part 1
23. Recognising quadratic equations with trigonometric functions – Part 2
24. Solving Quadratic Equations Involving Trig Functions

Radians

1. Introduction to Radians
2. Measuring Arc Length Part 1
3. Measuring Arc Length Part 2
4. Measuring the Area of a Sector Part 1
5. Measuring the Area of a Sector Part 2
6. Converting Between Different Units
7. Converting from Degrees to Radian Measure
8. Converting from Radian Measure to Degrees
9. What is a Radian?
10. Arc Length in Radian Measure
11. Area of a Sector in Radian Measure
12. Radian Mode and Trigonometry
13. Area of a Segment in Radian Measure
14. Hipparchus’ Triangles in Radians
15. The CAST Diagram in Radians
16. Trigonometric Curves in Radians
17. Solving Trigonometric Equations in Radian Measure
18. Degrees or Radians?

Small Angle Formulae

1. Introduction to Small Angle Formulae
2. What is a ‘Small Angle’?
3. Approximating Sin Part 1
4. Approximating Sin Part 2
5. Approximating Tan Part 1
6. Approximating Tan Part 2
7. Approximating Cos Part 1
8. Approximating Cos Part 2

Inverse Trig Functions

1. Introduction to the Inverse Trig Functions
2. Arcus Functions
3. The Inverses of Trig Functions
4. The Problem with Inverse Trig Functions
5. Restricting the Domains of Trig Functions (Part 1)
6. Restricting the Domains of Trig Functions (Part 2)
7. Memorising the Graph of the Inverse Sin Function
8. Memorising the Graph of the Inverse Cos Function
9. Memorising the Graph of the Inverse Tan Function

The Compound Angle Identities

1. Introduction to the Compound Angle Identities
2. What are Compound Angles?
3. The Compound Angle Identity for Sine
4. Finding More Outputs from the Sine Function
5. The Compound Angle Identity for Cosine
6. Finding More Outputs from the Cosine Function
7. Compound Angles with One Unknown
8. Solving More Trigonometric Equations
9. How Do We Simplify asinx + bcosx?
10. Dividing Equationss
11. Dividing and Simplifying Equations
12. Solving Simultaneous Trigonometric Equations Part 1
13. Solving Simultaneous Trigonometric Equations Part 2
14. Finding the Exact Value of y Part 1
15. Finding the Exact Value of y Part 2
16. Coefficients in Identities Are Always the Same
17. Equating Coefficients in Conditional Identities
18. Simplifying asinx + bcosx Part 1
19. Simplifying asinx + bcosx Part 2
20. Simplifying asinx + bcosx Part 3
21. Simplifying asinx + bcosx Part 4
22. Solving Harder Trigonometric Equations
23. The Compound Angle Identity for Tangent
24. Finding More Outputs from the Tangent Function
25. Solving More Trigonometric Equations Part 3
26. Solving More Trigonometric Equations Part 4
27. Proving the Compound Angle Identities
28. Proof Part 1: Side Lengths for the Three Triangles
29. Proof Part 2: The Secret Triangle
30. Proof Part 3: Proving the Sine and Cosine Identities
31. Proving the Tangent Identity

The Double and Half Angle Identities

1. Introduction to the Double and Half Angle Identities
2. What is a Double Angle?
3. The Sine Double Angle Identity
4. Using the Sine Double Angle Identity Part 1
5. Using the Sine Double Angle Identity Part 2
6. The Cosine Double Angle Identity Part 1
7. The Cosine Double Angle Identity Part 2
8. Using the Cosine Double Angle Identity Part 1
9. Using the Cosine Double Angle Identity Part 2
10. Using the Cosine Double Angle Identity Part 3
11. Using the Cosine Double Angle Identity Part 4
12. Using the Cosine Double Angle Identity Part 5
13. The Tangent Double Angle Identity
14. Using the Tangent Double Angle Identity Part 1
15. Using the Tangent Double Angle Identity Part 2
16. Using the Double Angle Identities with Other Angles
17. Finding the Half Angle Identities

Reciprocal Trig Functions

1. Introduction to the Reciprocal Functions
2. The Cosecant Function
3. Outputs from the Cosecant Function
4. Solving Equations with Cosecant Functions
5. The Secant Function
6. Outputs from the Secant Function
7. Solving Equations with Secant Functions
8. The Cotangent Function
9. Outputs from the Cotangent Function
10. Solving Equations with Cotangent Functions Part 1
11. Solving Equations with Cotangent Functions Part 2
12. Solving Equations with Multiple Reciprocal Functions
13. More Pythagorean Identities Part 1
14. Solving Equations with the Pythagorean Identities Part 1
15. More Pythagorean Identities Part 2
16. Solving Equations with the Pythagorean Identities Part 2
17. Memorising the Graph of the Cosecant Function
18. Memorising the Graph of the Secant Function
19. Memorising the Graph of the Cotangent Function
20. Where Do the Reciprocal Functions Get Their Names?
21. What Are Complementary Angles?
22. Tangents and Secants
23. Where Does Tangent Get Its Name?
24. Where Does Secant Get Its Name?
25. Where Does Cotangent Get Its Name?
26. Where Does Cosecant Get Its Name?
27. Proving the Pythagorean Identities

Parametric Equations

1. Introduction to Parametric Equations
2. What are Parametric Equations?
3. Parametric Functions Tables
4. The Coordinates Given by Parametric Equations
5. Sketching the Curves of Parametric Equations
6. Sketching Curves within a Restricted Domain
7. What is a Parameter?
8. Turning Parametric Equations into a Cartesian Equation
9. Taking Shortcuts When Finding Cartesian Equations
10. Turning Cartesian Equations into Parametric Equations
11. Trigonometric Parametric Equations
12. The Problem with Trigonometric Parametric Equations
13. Converting When the Trig Functions are the Same
14. Converting When the Trig Functions are Reciprocals
15. Using the Pythagorean Identity
16. A Faster Way to Use the Pythagorean Identity
17. Using the Other Pythagorean Identities
18. The Secret Power of the Reciprocal Identities Part 1
19. Parametric Equations We Can Convert So Far
20. Multiple Trig Functions in One Parametric Equation
21. Using the Double Angle Identities
22. Using the Compound Angle Identities
23. Negative Solutions to Parametric Equations
24. The Domain and Range of Parametric Equations
25. Finding Unknown Coordinates
26. Finding Points of Intersection with Parametric Curves
27. What if Both Curves Are Defined Parametrically?