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Pre-Calculus

Pre-Calculus . Why????. So Why Are You Doing This Again?. Majors that Require Calculus. Business (Business Calc.) Economics Accounting Finance Etc. Engineering (Calc. 3) All Fields Natural Sciences (Calc.) Medical School Dental School Veterinary School Biology/ Chem /Etc. .

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Pre-Calculus

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  1. Pre-Calculus Why????

  2. So Why Are You Doing This Again?

  3. Majors that Require Calculus • Business (Business Calc.) • Economics • Accounting • Finance • Etc. • Engineering (Calc. 3) • All Fields • Natural Sciences (Calc.) • Medical School • Dental School • Veterinary School • Biology/Chem/Etc. • Calculus is the foundation for things like measuring interest on a loan, marginal revenues, and costs in a business. • Understanding relationships between observations and data and maximizing efficiency for everyday items such as roads and dams requires methods from calculus. • Necessary to prove you are capable of overcoming the challenges of learning hard material.

  4. Majors that Require Calculus • Computer Science (Calc. 3) • All Fields • Psychology (Calc.) • Any specialization that results in a B.S degree vs. a B.A degree. • Physics (Calc. 3) • Meteorology • Astronomy • All direct Physics Programs • The general logical and analytical processes required in calculus are invaluable for the many careers available in computer science and programming. • A major in psychology puts a lot of emphasis on cognitive theory, which relies heavily on calculus. Additionally, many social psychology experiments conduct advanced statistical analyses that use calculus in their calculations. • The study of physics is essentially not possible without calculus.

  5. Majors that Require Calculus • Statistics (At least Calc. 2) • Actuarial Science • Biostatistics • Sports Analyst • Architecture Majors (Calc.) • Most well-known programs require at least Calc. 1 • Education (Calc.) • Math/Science Teacher • ANY teacher who wants an endorsement in math. • Calculus is useful for calculating rates of change, and so it's central to complex statistical analysis. • Calculus covers topics that help students better understand how to better plan building construction. • It is incredibly difficult to find a job in the Chicago suburbs/city. Most non-math teachers opt for an additional endorsement in math to be more marketable.

  6. 10.1 – Cosine and Sine Sum & Difference Formulas

  7. Learning Objectives • Find exact values of angles NOT on unit circle • Use the unit circle to help! • Simplify expressions • By condensing the sum/difference formulas • NO CALCULATORS

  8. Cosine Sum and Difference Formulas There are two main purposes for the addition formulas: finding exact values of trigonometric expressions and simplifying expressions to obtain other identities.

  9. Practice Teams – 4th Juan Shane Dom Greg Jessie Ben Tony Loren Andrew AJ Ian Arian Taylor Zach Dustin Bri Heather Christian Colleen Hunter Andres Preston Ryan Gabbi Keegan Connor

  10. Practice Teams – 7th Megan H. Conner Zach . Z Bobby Sarah Alexa Megan C. Miguel Olivia Emma DJ Hector Drake J. Shaw Fernanda Zach C. Drew Alyssa Nick B. Sam Wahida Jessica Alexis Kayla Jake Aspen Mike

  11. Example Set 1: Find the Exact Value • cos(15°) • sin(7π/12) • cos(405°)

  12. Example Set 2: Simplify the Expression

  13. Homework • (TB) pg. 373 #13-15, 18 – find exact value #2, 3, 6 – simplify the expressions

  14. 10.1 – Cosine Formulas Sum and Difference Formulas

  15. Homework Questions • Homework Quiz: Pg. 373 #2, 15

  16. Practice Teams – 4th Juan Shane Dom Greg Jessie Ben Tony Loren Andrew AJ Ian Arian Taylor Zach Dustin Bri Heather Christian Colleen Hunter Andres Preston Ryan Gabbi Keegan Connor

  17. Practice Teams – 7th Megan H. Conner Zach . Z Bobby Sarah Alexa Megan C. Miguel Olivia Emma DJ Hector Drake J. Shaw Fernanda Zach C. Drew Alyssa Nick B. Sam Wahida Jessica Alexis Kayla Jake Aspen Mike

  18. Group Challenge • Simplify the given expression: Suppose that sin α = 3/5 and sin β = 24/25, where 0< α < π/2 < β < π. Find sin (α + β).

  19. Group Challenge • Simplify the given expression: Suppose that tanα = 4/3 and tanβ = 12/5, where 0 0 0 < α < β < π/2. Find cos (α + β).

  20. Practice Activity

  21. Homework • (TB) pg. 373 #17, 20 – find exact value #4, 5 – simplify the expressions #28, 30 – simplify the expressions

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