Pre-Calculus Why????
So Why Are You Doing This Again?
Majors that Require Calculus
1. Business (Business Calc.)
▫ Economics▫ Accounting▫ Finance▫ Etc.
2. Engineering (Calc. 3)▫ All Fields
3. 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.
Majors that Require Calculus
4. Computer Science (Calc. 3)
▫ All Fields
5. Psychology (Calc.)▫ Any specialization that
results in a B.S degree vs. a B.A degree.
▫
6. 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.
Majors that Require Calculus
7. Statistics (At least Calc. 2)▫ Actuarial Science▫ Biostatistics▫ Sports Analyst
8. Architecture Majors (Calc.)
▫ Most well-known programs require at least Calc. 1
▫
9. 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.
10.1 – Cosine and Sine
Sum & Difference Formulas
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
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.
Practice Teams – 4th
Juan Shane
Tony Loren
Taylor
Zach
Hunter
Dustin
Andres
Dom Ben
Andrew
AJ
Bri Colleen
Preston
Ryan
Heather
Christian
Gabbi Keegan
Connor
Greg Jessie
Ian Arian
Practice Teams – 7th
Conner
MiguelMegan C.
Drake
J. Shaw
Sam
Fernanda
Wahida
Zach . Z
Alexa
Olivia Emma
Zach C.
Nick B.
Jessica Alexis
Drew Alyssa
Kayla Jake
Mike
Bobby Sarah
DJ Hector
Aspen
Megan H.
Example Set 1: Find the Exact Value
A. cos(15°)
B. sin(7π/12)
C. cos(405°)
Example Set 2: Simplify the Expression
Homework
•(TB) pg. 373 #13-15, 18 – find exact value #2, 3, 6 – simplify the
expressions
10.1 – Cosine FormulasSum and Difference Formulas
Homework Questions
•Homework Quiz: Pg. 373 #2, 15
Practice Teams – 4th
Juan Shane
Tony Loren
Taylor
Zach
Hunter
Dustin
Andres
Dom Ben
Andrew
AJ
Bri Colleen
Preston
Ryan
Heather
Christian
Gabbi Keegan
Connor
Greg Jessie
Ian Arian
Practice Teams – 7th
Conner
MiguelMegan C.
Drake
J. Shaw
Sam
Fernanda
Wahida
Zach . Z
Alexa
Olivia Emma
Zach C.
Nick B.
Jessica Alexis
Drew Alyssa
Kayla Jake
Mike
Bobby Sarah
DJ Hector
Aspen
Megan H.
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).
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).
Practice Activity
Homework
•(TB) pg. 373 #17, 20 – find exact value #4, 5 – simplify the
expressions#28, 30 – simplify the
expressions