MTH 082 Technical Mathematics 2

Lecture Hours: 4
Credits: 4

Offers the second course of a two-term technical mathematics sequence designed to meet the needs of technology students from various disciplines and provide the mathematical skills for solving applied problems in the technical fields of engineering, drafting, mechanical design, forestry and electronics. Covers trigonometric functions, oblique triangles, vectors, solutions of trigonometric equations and graphing of trigonometric functions, exponents and radicals, complex numbers, logarithmic and exponential functions and their applications.

Prerequisite: MTH 081 with a grade of C or better; or consent of instructor.
Student Learning Outcomes:

Use mathematical problem-solving techniques involving trigonometric functions, vectors, radicals, complex numbers, logarithmic and exponential functions; including techniques of graphical, symbolic, narrative, and tabular representations.
Create mathematical models of real-world situations using trigonometric functions, vectors, complex numbers, logarithmic and exponential functions.
Use inductive reasoning to develop mathematical involving trigonometric functions, vectors, radicals, complex numbers, logarithmic and exponential functions. Use deductive reasoning to verify and apply mathematical arguments involving these models.
Make mathematical connections to, and solve problems from, other disciplines involving trigonometric functions, vectors, radicals, complex numbers, logarithmic and exponential functions.
Use oral and written skills to individually and collaboratively communicate about applications involving trigonometric functions, vectors, radicals, complex numbers, logarithmic and exponential functions.
Use appropriate technology to enhance the mathematical thinking and understanding, to solve mathematical problems involving trigonometric functions, vectors, radicals, complex numbers, logarithmic and exponential functions, and judge the reasonableness of their results.
Do projects that encourage independent, nontrivial exploration of mathematical concepts involving trigonometric functions, vectors, radicals, logarithmic and exponential functions.

Content Outline

Trigonometric Functions
- Trigonometric Functions of Any Angle
- Inverse Trigonometric Functions
- Applications of Trigonometry
  - Arc length and area of sector
  - Linear and angular velocities
Vectors and Oblique Triangle Trigonometry
- Scalars and Vectors
- Graphical Representation of Vectors
  - Triangle method of adding vectors
  - Parallelogram method of adding vectors
  - Addition and subtraction of vectors using components
- Applications of Vectors
  - Vectors in construction technology
  - Vectors in navigation
  - Vectors in electricity
- Law of Sines
- Law of Cosines
Graphs of Trigonometric Functions
- Sine and Cosine Curves
- Phase Shift
- Composite Sine and Cosine Curves
- Applications of Trigonometric Graphs
Complex Numbers
- Rectangular Form
  - Imaginary unit and conjugates
  - Graphing complex numbers
  - Complex number operations in rectangular form
- Polar Form
  - Converting to polar form
  - Operation with polar form
- Exponential Form
  - Converting to exponential form
  - Operation with exponential form
- Complex Numbers in AC Circuits
Exponents and Radicals
- Fractional Exponents
- Properties of Radicals
  - Rationalizing denominator
  - Simplifying radicals
- Operations with Radicals
  - Addition and subtraction of radicals
  - Multiplying radicals with the same index
  - Multiplying radicals with the different indices
  - Radical Equations
Exponential and Logarithmic Functions
- Exponential Function
  - Graphing exponential functions; Asymptotes
  - Compound interest
  - The exponential function ex
  - Exponential growth and decay
- Logarithmic Functions
  - Graphing logarithmic functions
  - Common logs and natural logs
  - Logs of different bases
- Properties of Logarithms
- Exponential and Logarithmic Equations
- Graphing Using Semi-Log and Log Paper
Trigonometric Identities and Equations
- Basic Identities
  - Pythagorean identity
  - Proving identities
  - Using graphs to help verify identities
- The Sum and Difference Identities
- The Double- and Half- Angle Identities
- Trigonometric Equations