Topics in Trigonometry 

1-1              Radian and Degree Measure

  1. Describe angles

  2. Use radian measure

  3. Use degree measure

  4. Use angles to model and solve real-life problems

 

1-2              Trigonometric Functions:  TheUnit Circle

  1. Identify a unit circle and its relationship to real numbers

  2. Evaluate trigonometric functions using the unit circle

  3. Use the domain and period to evaluate sine and cosine functions

  4. Use a calculator to evaluate sine and cosine functions

 

1-3              Right Angle Trigonometry

  1. Evaluate Trigonometric Functions of acute angles

  2. Use the fundamental trigonometric identities

  3. Use a calculator to evaluate trigonometric functions

  4. Use trigonometric functions to model and solve real-life problems

 

1-4              Trigonometric Functions of any angle

  1. Evaluate trigonometric functions of any angle

  2. Use reference angles to evaluate trigonometric functions of angles

  3. Evaluate trigonometric functions of real numbers

 

1-5              Graphs of Sine and Cosine Functions

  1. Sketch the graphs of basic sine and cosine functions

  2. Use amplitude and period to help sketch the graph of sine and cosine functions

  3. Sketch translations of the graphs of sine and cosine functions

  4. Use sine and cosine functions to model real-life data

 

1-6              Graphs of other Trigonometric Functions

  1. Sketch the graphs of tangent functions

  2. Sketch the graphs of cotangent functions

  3. Sketch the graphs of secant and cosecant functions

  4. Sketch the graphs of damped trigonometric functions

 

1-7              Inverse Trigonometric Functions

  1. Evaluate the inverse sine function

  2. Evaluate the other inverse trigonometric functions

  3. Evaluate the compositions of trigonometric functions

 

1-8              Applications and Models

  1. Solve real-life problems involving right triangles

  2. Solve real-life problems involving directional bearings

  3. Solve real-life problems involving harmonic motion

 

Chapter 2        Analytic Trigonometry

 

2-1              Using Fundamental Identities

  1. Recognize and write the fundamental trigonometric identities

  2. Use the fundamental trigonometric identities to evaluate trigonometric functions

 

2-2              Verifying Trigonometric Identities

  1. Plan a strategy for verifying trigonometric identities

  2. Verify trigonometric identities

 

2-3              Solving Trigonometric Equations

  1. Using standard algebraic techniques to solve trigonometric equations

  2. Solve trigonometric equations of quadratic type

  3. Solve trigonometric equations involving multiple angles

  4. Use inverse trigonometric functions to solve trigonometric equations

 

2-4              Sum and Difference Formulas

  1. Use sum and difference formulas to evaluate trigonometric functions

  2. Use sum and difference formulas to verify trigonometric identities and to solve trigonometric equations

 

2-5              Multiple-Angles and Product-to-Sum Formulas

  1. Use Multiple-Angle formulas to rewrite and evaluate trigonometric functions

  2. Use power-reducing formulas to rewrite and evaluate trigonometric functions

  3. Use half-angle formulas to rewrite and evaluate trigonometric functions

  4. Use product-to-sum formulas to rewrite and evaluate trigonometric functions

 

Chapter 3        Additional Topics in Trigonometry

 

3-1              Law of Sines

  1. Use the Law of Sines to solve oblique triangles

  2. Find the areas of oblique triangles

  3. Use the Law of Sines to model and solve real-life problems

 

3-2              Law of Cosines

  1. Use the Law of Cosines to solve obliques triangles

  2. Use the Law of Cosines to model and solve real-life problems