10-804-196Trigonometry w Apps
Course Information
Description
Topics include the unit circle, trigonometric functions, graphs, identities, equations, inverse functions, solutions of triangles, complex numbers, polar coordinates, and vectors.
Total Credits
3
Course Competencies
  1. Analyze trigonometric functions
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    graph angles in standard position
    solve problems involving special right triangles
    use reference angles to find exact values of trigonometric functions in any quadrant
    find the exact value of a trigonometric function given a point on the terminal side of an angle
    find the exact value of a trigonometric function given a right triangle
    use reciprocal identities
    use quotient identities
    use Pythagorean identities
    use even-odd identities
    use cofunction identities

  2. Evaluate the trigonometric functions
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    identify exact values of trigonometric functions
    find approximate values of trigonometric functions using a calculator
    solve right triangles using inverse trigonometric functions
    solve right triangles using trigonometric functions

  3. Apply the unit circle and radian measure
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    use the concept of a reference angle
    graph angles in standard position given radian measure
    relate radian measures to real numbers
    convert between radian measures and degree measures of angles
    find exact and approximate values of trigonometric functions given in radian measure
    analyze the unit circle
    find arc length and area of a sector

  4. Analyze graphs of trigonometric functions
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    sketch graphs of basic trigonometric functions
    apply transformations to the graphs of trigonometric functions
    identify domains and ranges of trigonometric functions and their graphs
    identify domains and ranges of graphs of trigonometric functions
    find equations from graphs of trigonometric functions

  5. Analyze inverse trigonometric functions
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    define the inverse trigonometric functions
    identify domains and ranges of inverse trigonometric functions
    sketch graphs of the inverse trigonometric functions
    evaluate the inverse trigonometric functions
    evaluate the composition of trigonometric and inverse trigonometric functions

  6. Manipulate trigonometric identities
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    use identities to evaluate trigonometric functions
    use trigonometric identities to verify other identities
    apply sum and difference identities
    apply double-angle and half-angle identities
    apply sum-to-product and product-to-sum identities

  7. Solve trigonometric equations
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    solve equations involving trigonometric expressions of a single angle
    solve equations involving trigonometric expressions of multiple angles
    use correct notation to express infinite and finite solution sets of trigonometric equations

  8. Solve oblique triangles
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    use the Law of Sines to solve oblique triangles
    use the Law of Cosines to solve oblique triangles
    calculate areas of oblique triangles
    solve application problems involving oblique triangles

  9. Perform vector operations
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    define a vector
    define unit vectors i and j
    identify the horizontal and vertical components of a vector
    find the magnitude of a vector
    find the direction of a vector
    perform vector addition
    perform scalar multiplication of vectors
    compute dot product of vectors
    determine if two vectors are perpendicular
    find the angle measure between two vectors

  10. Perform operations with complex numbers in trigonometric form
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    convert complex numbers between rectangular form and trigonometric form
    graph complex numbers in trigonometric form and rectangular form
    find products of complex numbers written in trigonometric form
    find quotients of complex numbers written in trigonometric form

  11. Analyze the polar coordinate system
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    identify points in the polar coordinate system
    translate between rectangular coordinates and polar coordinates for a given point
    convert an equation between polar form and rectangular form
    explore graphs of equations in polar form