Title: Module 4 Basic Trig Properties, Vectors & Logarithms
Course: Technical Math for Industry > Section: Module 4.0: Trigonometry, Vectors and Logarithms

Overview and Introduction

This module contains interactive tutorials to help you practice or refresh your math skills on the following topics:

Trigonometry Functions

Lesson 34 Learning Objectives-Introduction to Trigometric Functions

- Identifying the Six Trigonometric Functions
  - Identify the hypotenuse, adjacent side, and opposite side of an acute angle in a right triangle.
  - Determine the six trigonometric ratios for a given angle in a right triangle.
  - Recognize the reciprocal relationship between sine/cosecant, cosine/secant, and tangent/cotangent.
  - Use a calculator to find the value of the six trigonometric functions for any acute angle.
  - Use a calculator to find the measure of an angle given the value of a trigonometric function.

- Right Triangle Trigonometry
  - Use the Pythagorean Theorem to find the missing lengths of the sides of a right triangle.
  - Find the missing lengths and angles of a right triangle.
  - Find the exact trigonometric function values for angles that measure 30°, 45°, and 60°.
  - Solve applied problems using right triangle trigonometry.

- Unit Circle Trigonometry
  - Understand unit circle, reference angle, terminal side, standard position.
  - Find the exact trigonometric function values for angles that measure 30°, 45°, and 60° using the unit circle.
  - Find the exact trigonometric function values of any angle whose reference angle measures 30°, 45°, or 60°.
  - Determine the quadrants where sine, cosine, and tangent are positive and negative.

Lesson 35 Learning Objectives-Graphing Trigonometric Functions

- Degree and Radian Measure
  - Understand radian measure.
  - Convert from degree to radian measure.
  - Convert from radian to degree measure.

Graphing the Sine and Cosine Functions
  - Determine the coordinates of points on the unit circle.
  - Graph the sine function.
  - Graph the cosine function.
  - Compare the graphs of the sine and cosine functions.

Amplitude and Period
  - Understand amplitude and period.
  - Graph the sine function with changes in amplitude and period.
  - Graph the cosine function with changes in amplitude and period.
  - Match a sine or cosine function to its graph and vice versa.

Exponential and Logarithmic Functions

Lesson 36 Learning Objectives-Exponential Functions

- Introduction to Exponential Functions
  - Graph exponential equations and functions.
  - Solve applied problems using exponential problems and their graphs.

Lesson 37 Learning Objectives-Logrithmic Functions

- Introduction to Logarithmic Functions
  - Convert logarithmic equations to exponential equations.
  - Convert exponential equations to logarithmic equations.
  - Graph logarithmic functions.
  - Solve logarithmic equations.

Properties of Logarithmic Functions
  - Express the logarithm of a product as a sum of logarithms.
  - Express the logarithm of a quotient as a difference.
  - Express the logarithm of a power as a product.
  - Simplify logarithmic expressions.

Lesson 38 Learning Objectives-Natural Logarithms

- Introduction to Natural and Common Logarithms
  - Use a calculator to find logarithms or powers of base e.
  - Graph exponential and logarithmic functions of base e.
  - Find logarithms to bases other than e or 10 by using the change of base formula.

Lesson 39 Learning Objectives-Logarithmic and Exponential Equations

- Solving Exponential and Logarithmic Equations
  - Solve exponential equations.
  - Solve logarithmic equations.
- Mathematical Modeling with Exponential and Logarithmic Functions
  - Solve applied problems involving logarithmic functions.
  - Solve applied problems involving exponential functions.

The lessons are designed to be self-paced and accomplished at your own pace.

If you have taken the Math Readiness Quiz, you will understand where your math strengths and weakness are and can tailor your learning to just the topics and modules you need. You may review the material as many times as you need and take the quizzes as many times as needed to increase your proficiency in the math concept.