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