TRIGONOMETRY, EXPONENTS & LOGARITHMS
UNIT RESOURCES: TRIGONOMETRY
- Daily Plan ( Trig, Exp and Logs)
- Review: Identities & Equations
- Lesson Package
- Calculus - A First Course, James Stewart. McGraw-Hill Ryerson, 1989: Chapter 6 & Chapter 7
Quizzes and Homework:
- Exams:
- 2023: Exam and Answer Keys
- Trig Check For Understanding
- Trig 1 and Answer Key
- Trig 2 and Answer Key
- Trig 3 and Answer Key
- Trig 4 and Answer Key
- 2019 Trig Quiz 1 and Answer Key
- 2020 Trig Summary and Answer Key
- Exp & Log Check for Understanding
- Exp/Log 1 and Answer Key
- Exp/Log 2 and Answer Key
- Quiz 2013 and Answer Key
- Quiz 2018 and Answer Key
- Summary 2020 and Answer Key
- Quizzes
- Review:
- Trig Identities
- Trig Equations
Trig Limits
Divide by zero or not divide by zero:
Divide by zero or not divide by zero:
- Not divide by zero, then we can substitute as the function is continuous
- Zero divide by zero - is a good thing too; we just need to simplify using algebraic methods
Derivatives of Sine and Cosine.
Visual - use the graph of y=sinx to find the graph of the slopes. Use the graph of y=cosx to find the graph of the slopes.
Limits - use First Principles to find dy/dx for y=sinx.
Notes: Original [Derivatives examples part 1] [derivative examples part 2]
- Examples (Notes)
- Text Video: [1h, 1p]
Derivatives of other trig ratios:
Express ratios in terms of sinx and/or cosx to find their dy/dx.
Once you know the base derivatives, we apply the chain rule, product rule, quotient rule etc to find dy/dx of trig expressions/equations.
Notes: Original [Derivative of TAN, SEC, CSC, COT video]
We can apply the First Derivative Rule and/or the Second Derivative Rule to find maximum and/or minimum values of trig functions.
Trig Check for Understanding
- Trig 1 and Answer Key [video Q3]
- Trig 2 and Answer Key
- Trig 3 and Answer Key [video 1b]
Problem Solving.
Try the following steps to solve your problems:
- Draw a diagram, label things that change with variables.
- Match the number of variables to the number of rates in the problem.
- Determine which trig ratio to work with - you may have two choices, select the easiest one to derive.
- Put rates into the question - usually time... d/dt.
- Solve for the moment - usually you need to solve for one piece of the puzzle on your own.
Trig Review
- Trig 4 and Answer Key [video Q2]
- 2019 Trig Quiz 1 and Answer Key [Video 1a]
- Trig Summary Assignment [May 2020] [Summary Key]
Exponents and Logarithms
Exponents and Logarithms
Exponents and Logarithms 2020
- Daily Plan (Trig, Exp and Logs)
- Review: Logarithm Functions
- Lesson Package
- Calculus - A First Course, James Stewart. McGraw-Hill Ryerson, 1989. Chapter 8
Review of Exponential Functions and Logarithms: properties (domain, range, intercepts) and simplifying/solving.
Introduction to base "e". The derivative of exponential functions, base e.
Notes: Original
Notes: Original
- Story of e [video]
- Derivative of y=e^x [video] [derivative proof]
- Examples
- 2018 Examples
Natural Logarithms. The derivative of logarithms, base = e.
Notes: Original
Notes: Original
- Logarithmic Functions with base 'e' . [Video]
- Derivative of y=ln(x) [Video Examples 1abcd] [Examples 1ef] [not base e examples] [derivative proof]
- Examples
Derivatives of exponential and logarithmic functions when the base is not 'e'.
Logarithmic Differentiation - take the natural log of complicated functions and apply the derivative of ln rules.
Notes: Original [Video Intro & Example 1] [Examples 2, 3a] [Example 3b and 2018 Exam Examples]
Logarithmic Differentiation - take the natural log of complicated functions and apply the derivative of ln rules.
Notes: Original [Video Intro & Example 1] [Examples 2, 3a] [Example 3b and 2018 Exam Examples]
Exp & Log Checks for Understanding
- Exp and Logs 1 and Answer Key
- Exp and Logs 2 and Answer Key
- Quiz 2013 and Answer Key
- 2018 Exp & Log Quiz and Answer Key
Exponents and Log Summary Assignment
- [June 2020] [Answer Key]