Download Final Exam Review Sheet Chapter 1 • The Distance Formula • The

Final Exam Review Sheet
Chapter 1
• The Distance Formula
• The Theorem on Circles - the equation of a circle
• Definition of a Function (and function vocabulary)
• Domains and Ranges
Review Problems: Chapter 1 Review 6,7, 17, 18, 19, 20, 40-45, 46, 47, 52, Exam 1
Chapter 2
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Definition of Principle Trigonometric Ratios (for all angles, radians and degrees)
Definition of Reciprocal Trig Ratios (for all angles)
Evaluating Trig Ratios (For all angles)
Solve all the types of right triangles
Application Problems
Reference angles
– Using reference angles to evaluate trig ratios
– Using reference angles to help solve equations!!!
• Definition of radians
• Converting between degrees and radians
Review Problems: Chapter 2 review 2, 3-6, 41-49, 53-55, 59-60, 73-76, 77-80, 81-82, 89-92, 99-104,
Exam 1 and Exam 2
Chapter 3
• The Unit Circle!
• Evaluate trig functions exactly for real numbers
• Graph of Sine, Cosine, Tangent, Cotangent, Secant, Cosecant
• Amplitude, period, phase shift
• Graphing sine and cosine with amplitude changes, period changes, and phase shifts!
• Definition of arcsin(x), arccos(x), arctan(x).
• Domains and ranges of inverse trig functions
• Evaluating the inverse trig functions exactly
• Evaluating expressions involving both inverse trig functions and trig functions exactly
Review problems: Chapter 3 review 2-3, 6-8, 16-19, 22-27, 28-30, 34, 35, 36, 39, 41,42, 43, 44, 47-54,
Exam 2
Chapter 4
(1) Section 4.1
• Reciprocal Identities
• Quotient Identities
• Pythagorean Identities
• Prove Basic identities
Review Problems: Chapter 4 review: 2-3, 5, 6, 7, 8, 9-14
(2) Section 4.2
• Solve Trig equations of the following types
– basic (trig function=number)
– quadratic
– using an inverse function
– using basic identities
Review Problems: Chapter 4 review: 17-26, 27-32, 33-40, 41-46, 47-54 (don’t need to graph),
55-58
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(3) Section 4.3
• Sum and difference Identities
• Using sum and difference Identities to find exact cos, sin tan values.
– of a given angle. (sin(105◦ ))
– when given the sin or cos of α and β (see example 5)
• Rewriting\Simplifying Identities (see example 6)
• Negative angle identities
• Cofunction identities
Review Problems: Chapter 4 review: 59-62, 63-66, 67-69, 71-76, 83, 84, 85,
(4) Section 4.4
• Double angle Identities
• Half angle Identies
• Using double angle and half angle Identities to find exact cos, sin tan values.
– of a given angle. (sin(π/8))
– when given the sin or cos of α and β (see example 1\5)
• Rewriting\Simplifying Identities (see example 2)
• Solving equations using these identities (see example 4)
Review Problems: Chapter 4 review: 77, 78, 79, 80, 81, 82, 86, 87,
Chapter 5
(1) Section 5.1
• Area formula
• Law of Sines
– find a side using the law
– find an angle using the law (be careful about the number of angles!)
• Application problems
Review Problems: Chapter 5 review: 2-5, 15-17, 19 20, 21
(2) Section 5.2
• Law of cosines
– find a side using the law
– find an angle using the law
• Heron’s Formula (for area)
• Solving Triangles
• Application problems
Review Problems: Chapter 5 review: 6-9, 10-14, 18, 22, 23, 24,