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 2 radians Example Convert 250 to radians Example Convert 3 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 2 sin 3 Unit Circle 2 cos 3 2 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 cos sin2 cos2 1 sin 2x 2 sin x cos x tan2 1 sec2 tan 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 3 with x 0 find sin 2x 2 2 Example Solve the following equations for x where 0 x 2 A 2 cos x 1 0 B 2 cos x sin 2x 0
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