10.1 – Sine & Cosine Formulas

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

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.

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 #1-5 odd – simplify the expressions

#13-19 odd – find exact value

10.1 – Sine and Cosine FormulasSum and Difference Formulas

Homework

•TB pg. 373 #1-5 odd – simplify the expressions

#13-19 odd – find exact value

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

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).

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.

Homework

•TB pg. 373 #7, 9 – prove #25-29 odd– simplify the

expressions