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Page 1 Math 152-copyright Joe Kahlig, 11C Review of Functions and Appendix D Functions: A function, f , is a rule that assigns to each element, x, in set A exactly one element, called f (x), in set B. The set A is called the domain. The range of f is the set of all possible values of f (x) where x is in the domain, i.e. range = { f (x)|x ∈ A }. Example: Find the domain of f (x) = Example: Find the domain of y = √ x x2 − 25 x2 1 − 2x − 24 Example: Express y = |x − 5| without the absolute value symbols. Example: Express y = |x2 − 4| without the absolute value symbols. Appendix D: Trigonometry Angles can be measured in degrees or radians. Thus 360o = 2π radians Example: Convert 250 to radians. Example: Convert −3π to degrees. 4 Page 2 Math 152-copyright Joe Kahlig, 11C Trigonometric Functions: Consider the right triangle. hypotenuse sin A = opp hyp cos A = adj hyp tan A = opp adj csc A = hyp opp sec A = hyp adj cot A = adj opp opposite A adjacent Special Triangles: 45-45-90 and 30-60-90. Example: Evaluate the following: 2π sin 3 = Unit Circle: 2π cos 3 = 2π tan 3 = Page 3 Math 152-copyright Joe Kahlig, 11C Trigonometric Identities: These identities are used some in Math 151, but are use a lot in Math 152. sin θ cos θ sin2 θ + cos2 θ = 1 sin(2x) = 2 sin x cos x tan2 θ + 1 = sec2 θ tan θ = 1 + cos(2x) 2 1 − cos(2x) sin2 x = 2 cos2 x = cos(2x) = 2 cos2 (x) − 1 Law of sines: B sin A sin B sin C = = a b c a c Law of cosines: a2 = b2 + c2 − 2bc cos A C A b Example: If sec(x) = Law of cosines: b2 = a2 + c2 − 2ac cos B Law of cosines: c2 = a2 + b2 − 2ab cos C −π 3 with < x < 0, find sin(2x) 2 2 Example: Solve the following equations for x where 0 ≤ x ≤ 2π A) 2 cos(x) − 1 = 0 B) 2 cos(x) + sin(2x) = 0