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