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- Introduction to Angles in Trigonometry
- Standard Position of an Angle
- Angles Measured in Degrees
- Angles Measured in Degrees, Minutes, and Seconds
- Angles Measured in Radians
- Coterminal Angles
- Converting Degrees to Radians and Radians to Degrees
- Common Angles in Degrees and Radians
- Finding the Arc Length of a Circle
- Finding the Area of a Sector
- Finding the Linear and Angular Speed in Circular Motion
- Finding the Distance Between Two Cities

- The Unit Circle
- Creating the Unit Circle
- Finding Trigonometric Values Using the Unit Circle
- Finding Trigonometric Values of Quadrant Angles Using the Unit Circle
- Trigonometric Values of Common Angles
- Evaluating Trigonometric Expressions
- Using a Circle with Radius r to Evaluate Trigonometric Values
- Trigonometric Signs in Different Quadrants
- Finding All Six Trigonometric Values Given Sine and Cosine Values
- Finding All Six Trigonometric Values Given One (x,y) Point
- Finding All Six Trigonometric Values Given One and the Sign of Another
- Reference Angles
- Finding Trigonometric Values Using Reference Angles

- Introduction to Sinusoidal Graphs
- Basic Sine and Cosine Graphs
- The Amplitude of Sine and Cosine Graphs
- The Period of Sine and Cosine Graphs
- Horizontal Phase Shifts (Translations) of Sine and Cosine Graphs
- Vertical Phase Shifts (Translations) of Sine and Cosine Graphs
- Determining the Equation of a Sinusoidal Graph
- Graphing Tangent Functions
- Graphing Cotangent Functions
- Graphing Cosecant and Secant Functions
- Simple Harmonic Motion

- Inverse Sine Function
- Composition of Sine and Inverse Sine Functions
- Inverse Cosine Function
- Composition of Cosine and Inverse Cosine Functions
- Inverse Tangent Function
- Composition of Tangent and Inverse Tangent Functions
- Composition of Inverse Functions (Sine, Cosine, Tangent)
- Inverse Cosecant, Inverse Secant, and Inverse Cotangent
- Composition of Inverse Functions (Cosecant, Secant, and Cotangent)
- Using a Calculator to Evaluate Inverse Cosecant, Inverse Secant, and Inverse Cotangent Expressions

- Reciprocal, Quotient, and Pythagorean Identities
- Simplifying Expressions with the Reciprocal, Quotient, and Pythagorean Identities
- Proving Identities with the Reciprocal, Quotient, and Pythagorean Identities
- Even and Odd Identities
- Proving More Trigonometric Identities
- Factoring and FOILing to Prove Trigonometric Identities

- Sum and Difference Sine Formulas (Finding Exact Values)
- Sum and Difference Cosine Formulas (Finding Exact Values)
- Sum and Difference Tangent Formulas (Finding Exact Values)
- Using Sum and Difference Formulas
- Using Sum and Difference Formulas with Inverse Functions
- Proving Identities Using Sum and Difference Formulas
- Double Angle Sine Formula
- Double Angle Cosine Formulas
- Double Angle Tangent Formulas
- Power-Reducing Formulas
- Half-Angle Sine Formula
- Half-Angle Cosine Formula
- Half-Angle Tangent Formula
- Using Double Angle and Half Angle Formulas with Inverse Functions
- Product-to-Sum Formulas
- Sum-to-Product Formulas

- Using Reference Angles to Solve Trigonometric Equations
- Finding All Solutions of Trigonometric Equations
- Solving Basic Trigonometric Equations
- Solving Trigonometric Equations by Combining Like Terms
- Solving Trigonometric Equations by Taking the Square Root
- Solving Trigonometric Equations by Factoring
- Solving Trigonometric Equations with an Argument of 2?ΒΈ
- Solving Trigonometric Equations with an Argument of ?/2
- Solving Trigonometric Equations with an Argument Expression
- Solving Trigonometric Equations Using Identities

- Right Triangle Trig Ratios
- Complementary Angle Theorem with Trigonometry
- Solving Word Problems Using Right Triangle Trigonometry
- Law of Sines
- The Ambiguous Case for the Law of Sines
- Trigonometry Fomula for the Area of a Triangle
- Law of Cosines
- Heron's Formula for the Area of a Triangle
- Finding the Area of Quadrilaterals
- Navigation Problems (Direction and Bearing)

- Introduction to Vectors
- Properties of Adding Vectors
- The Negation of a Vector and Subtracting Vectors
- Scalar Multiplication with Vectors
- Vectors in Standard Position and Finding Position Vectors
- Vectors in Component Form
- Operations with Vectors in Component Form
- Magnitude of Vectors in Component Form
- Finding the Direction of a Vector in Component Form
- The Unit Vector in the Same Direction as v = (a,b)
- Vectors in ai + bj Form
- Operations with Vectors in ai + bj Form
- Magnitude of Vectors in ai + bj Form
- Finding the Direction of a Vector in ai + bj Form
- The Unit Vector in the Same Direction as v = ai + bj
- Finding the Horizontal and Vertical Components of a Vector
- The Dot Product of Two Vectors
- Finding the Angle Between Two Vectors
- Parallel Vectors
- Perpendicular (Orthogonal) Vectors

- Definition of Polar Coordinates and Plotting Polar Coordinates
- Plotting Polar Coordinates on a Polar Grid
- Finding Different Polar Coordinates for Same Point
- Converting Polar Coordinates to Rectangular Coordinates
- Converting Rectangular Coordinates to Polar Coordinates
- Transforming an Equation from Polar Form to Rectangular Form
- Transforming an Equation from Rectangular Form to Polar Form
- Graphing Polar Equations