1. Your petition
2. Solving Trigonometric Equations with Identities
3. Sum and Difference Identities
4. Double-Angle, Half-Angle, and Reduction Formulas
5. Sum-to-Product and Product-to-Sum Formulas
6. Solving Trigonometric Equations
7. Modeling with Trigonometric Equations

• Teaching methods
• The set up of the room
• Computers are a distraction
• Want to work with paper with pencil
• ???

• Pass this course
• Supplement knowledge
• Prepare for other courses
• Assist in career suubjects
• Solve difficult problems with ease
• Able to explain math
• Develop a love for math
• Learn something new and practical

• Help each other
• Understand respect each other
• Work collectively
• Work on effective communications
• Come ready to discuss the topic
• Commitment to achieve goals

• Who is this petition addressed to?
• What opinions/resources have you already explored?
• What do you really want?

\[ \large\begin{array}{rcl} \sin\theta &=& \cos\left({\pi\over 2} - \theta\right) \\ \\ \cos\theta &=& \sin\left({\pi\over 2} - \theta\right) \\ \\ \tan\theta &=& \cot\left({\pi\over 2} - \theta\right) \\ \end{array} \]

\[ \large\begin{array}{rcl} \sin\left({\theta\over 2}\right) & = & \pm \sqrt{1- \cos(\theta)\over 2}\\ \\ \cos\left({\theta\over 2}\right) & = & \pm \sqrt{1 + \cos(\theta)\over 2}\\ \\ \tan\left({\theta\over 2}\right) & = & \pm \sqrt{1 - \cos(\theta)\over 1 + \cos(\theta)} = {\sin(\theta) \over 1 + cos(\theta)} = {1 - cos(\theta)\over \sin(\theta)}\\ \end{array} \]

\[ \large\begin{array}{rcl} \sin\left(2\theta\right) & = & 2 \sin(\theta) \cos(\theta)\\ \\ \cos\left(2\theta\right) & = & \cos^2(\theta) - \sin^2(\theta) = 1 - 2 \sin^2(\theta) = 2 \cos^2(\theta) - 1\\ \\ \tan\left(2\theta\right) & = & {2 \tan(\theta)\over 1 - \tan^2(\theta)} \\ \end{array} \]

\[ \large\begin{array}{rcl} \sin^2 \theta & = & {1 - \cos(2\theta)\over 2}\\ \\ \cos^2 \theta & = & {1 + \cos(2\theta)\over 2}\\ \\ \tan^2 \theta & = & {1 - \cos(2\theta)\over 1 + \cos(2\theta)}\\ \end{array} \]

\[ \large\begin{array}{rcl} \sin(\alpha + \beta) & = & \sin\alpha \cos\beta + \cos\alpha \sin\beta\\ \\ \cos(\alpha + \beta) & = & \cos\alpha \cos\beta - \sin\alpha \sin\beta\\ \\ \tan(\alpha + \beta) & = & {\tan\alpha + \tan\beta\over 1 - \tan\alpha \tan\beta}\\ \end{array} \]

Difference \[ \large\begin{array}{rcl} \sin(\alpha - \beta) & = & \sin\alpha \cos\beta - \cos\alpha \sin\beta\\ \\ \cos(\alpha - \beta) & = & \cos\alpha \cos\beta + \sin\alpha \sin\beta\\ \\ \tan(\alpha - \beta) & = & {\tan\alpha - \tan\beta\over 1 + \tan\alpha \tan\beta}\\ \end{array} \]

\[ \large\begin{array}{rcl} \cos\alpha \cos \beta & = & {\cos(\alpha -\beta) + \cos(\alpha + \beta)\over 2}\\ \\ \sin\alpha \sin \beta & = & {\cos(\alpha -\beta) - \cos(\alpha + \beta)\over 2}\\ \\ \sin\alpha \cos \beta & = & {\sin(\alpha +\beta) + \sin(\alpha - \beta)\over 2}\\ \\ \cos\alpha \sin \beta & = & {\sin(\alpha +\beta) - \sin(\alpha - \beta)\over 2}\\ \end{array} \]

• Names and roles of team members
• List the time and angle data collected for both teams
  • the angle between the ground and the balloon
  • the angle between the balloon and the other measuring team
• List of the calculated distance and height
• A plot of the flight path
• Submit the report before class on 8 Nov

• Names of the team member
• Test data from experiments with 10 rubber bands
• Plot of the stretch achieved for 1 to 10 bands
• The linear model suggested by the data
• Predicted number of rubber bands and the test results
• A group picture of the team assembling the bungee chord
• Printed submitted before class on 8 Nov
• Worth 5 points of the course