Exam 2 Study Guide - Trigonometry | MATH 229, Exams of Trigonometry

Download Exam 2 Study Guide - Trigonometry | MATH 229 and more Exams Trigonometry in PDF only on Docsity! Math 229 EXAM 2 STUDY GUIDE DEFINITIONS AND VOCABULARY: Reference triangle and reference angle (p110) Radian (p118) Function, domain and range (p446) Relation (p447) Circular functions (p131) Domains and ranges of the circular functions (p135) Period and amplitude (p172) Zero of a function (p173) Six basic cycles and their properties (p179) Even and odd function (p180) Phase shift (p200) Inverse relation and inverse function (p455, 459) One-to-one function (p458) Inverse trigonometric functions (p242) FORMULAS 180° = π radians Arc Length: s rθ= (θ in radians) Sector Area: 212A r θ= (θ in radians) IDENTITIES sin( ) sinθ θ− = − cos( ) cosθ θ− = tan( ) tanθ θ− = − CONCEPTS AND THEOREMS On the unit circle, (x, y) = (cos t, sin t) where t is the arc length (angle in radians) Vertical line test (p447) Symmetry property of inverses (p456) Horizontal line test (p458) YOU SHOULD BE ABLE TO: Find the reference angle for a given angle in standard position Convert from radians to degrees and vice-versa (by hand and using your calculator) Find exact values of the six trigonometric ratios for an angle in radians or degrees using the reference angle Find approximate values of the six trigonometric ratios using your calculator in radian or degree mode Find the angle (by hand) in degrees or radians given the value of a trigonometric ratio Approximate the angle (using your calculator) in degrees or radians given the value of a trigonometric ratio Find exact values of the six trigonometric functions using the unit circle Find a point on the unit circle given the arc length or angle in radians Find the angle (in radians) corresponding to a given point on the unit circle Solve problems and applications involving arc length or sector area Verify identities involving the negative angle identities State the amplitude, period, domain, and range for the six trigonometric functions Graph the six basic cycles (by hand) and identify intercepts and asymptotes Identify the amplitude, period and phase shift for a trigonometric function Graph trigonometric functions (by hand) showing one complete cycle in detail Find an equation for a trigonometric function (sine or cosine) given its graph Find the equation for the inverse of a relation Graph the inverse of a relation using the symmetry property Determine graphically if a function is one-to-one State the domain and range for the inverse trigonometric functions (sine, cosine, and tangent) Graph (by hand) the basic inverse trigonometric functions (sine, cosine, and tangent) Evaluate (by hand) an inverse trigonometric function exactly (sine, cosine, and tangent) Approximate (using a calculator) an inverse trigonometric function (sine, cosine, and tangent) Simplify expressions involving inverse trigonometric functions Write an expression involving inverse trigonometric functions in terms of x only EXTRA PRACTICE Chapter 3 Test (p164-166): 1-21, 23 Chapter 4 Test (p252-253): 1-19, 22-30