Unit 3
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Lesson 1: The fundamental Trigonometric Identities
Six trigonometric ratios (6)
Quotient identities (2)
Pythagorean identity (3)
Even/Odd identities (6)
Odd: sin, csc, tan, cot
Even: cos, sec
Lesson 2: Verifying trigonometric identities
Guidelines for verifying identities
Working on one side only
Look for fundamental identities
Factor, add, subtract, and conjugate
Change everything to sine and cosine when everything fails
Lesson 3: Solving advanced trigonometric equations
Lesson 4: Graphing trigonometric functions
Lesson 5: Sum, difference, and double angle identities
Rules
Algebraically verify even/odd property
Start with f(−x), see whether it can be simplifed into f(x) or −f(x)
Lesson 6: Harmonic motion
Simple harmonic motions: described by sinusoidal function
y=a⋅sin(b(x−h)+k
Amplitude: a
Number of cycles in a period: b (period: 2π/b)
Horizontal shift: h
Vertical shift: k