Math 152-copyright Joe Kahlig, 11C Page 1Review of Functions and Appendix DFunctions: 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 s et of all possible valuesof f (x) where x is in the domain, i.e. range = { f (x)|x ∈ A }.Example: Find the domain of f (x) =xx2− 25Example: Find the domain of y =1√x2− 2x − 24Example: Express y = |x − 5| without the absolute value symbols.Example: Express y = |x2− 4| without the ab solute value symbols.Appendix D: TrigonometryAngles can be measur ed in degrees or r ad ians . Thus 360o= 2π radiansExample: Convert 250to radians.Example: Convert−3π4to degrees.Math 152-copyright Joe Kahlig, 11C Page 2Trigonometric Functions: Consider th e right triangle.adjacentAhypotenuseoppositesin A =opphypcos A =adjhyptan A =oppadjcsc A =hypoppsec A =hypadjcot A =adjoppSpecial Triangles: 45-45-90 and 30-60-90.Example: Evaluate the f ollowing:sin2π3= cos2π3= tan2π3=Unit Circle:Math 152-copyright Joe Kahlig, 11C Page 3Trigonometric Identities: These identities are used some in Math 151, but are use a lot in Math 152.tan θ =sin θcos θsin2θ + cos2θ = 1 cos2x =1 + cos(2x)2sin(2x) = 2 sin x cos x tan2θ + 1 = sec2θ sin2x =1 −cos(2x)2cos(2x) = 2 cos2(x) −1ABCabcLaw of sines:sin Aa=sin Bb=sin CcLaw of cosines: a2= b2+ c2− 2bc cos ALaw of cosines: b2= a2+ c2− 2ac cos BLaw of cosines: c2= a2+ b2− 2ab cos CExample: If sec(x) =32with−π2< x < 0, find sin(2x)Example: Solve the following equations for x wher e 0 ≤ x ≤ 2πA) 2 cos(x) − 1 = 0B) 2 cos(x) + sin(2x) =
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