Exam 1 Study Guide for Trigonometry | MATH 229, Exams of Trigonometry

Download Exam 1 Study Guide for Trigonometry | MATH 229 and more Exams Trigonometry in PDF only on Docsity! Math 229 EXAM 1 STUDY GUIDE DEFINITIONS AND VOCABULARY Degree, minutes, seconds (p3, 61) Acute, right, obtuse, and straight angles (p3) Complementary and supplementary angles (p3) Isosceles, equilateral, scalene, acute, and obtuse triangles (p4) Right triangle, legs and hypotenuse (p5) Standard position for an angle, positive and negative angles (p20) Quadrant and quadrantal angles (p21) Coterminal angles (p21) Trigonometric ratios using x, y, and r (p27) Identity (p33) Trigonometric ratios using opposite, adjacent, and hypotenuse (p54) Cofunctions (p55) Angle of elevation or depression (p81) Bearing (p84) Scalar vs vector (p93) Magnitude or norm of a vector (p93) Resultant vector (p94) Horizontal and vertical vector components (p96) Static equilibrium (p98) FORMULAS Circle: 2 2 2( ) ( )x h y k r− + − = Work = d⋅F sinθ = y/r cosθ = x/r tanθ = y/x cscθ = r/y secθ = r/x cotθ = x/y sinθ = opp/hyp cosθ = adj/hyp tanθ = opp/adj cscθ = hyp/opp secθ = hyp/adj cotθ = adj/opp IDENTITIES 1sin csc θ θ = 1cos sec θ θ = 1tan cot θ θ = sintan cos θθ θ = coscot sin θθ θ = 2 2sin cos 1θ θ+ = 2 2tan 1 secθ θ+ = 2 21 cot cscθ θ+ = 2sin 1 cosθ θ= ± − 2cos 1 sinθ θ= ± − sin cos(90 )θ θ= °− cos sin(90 )θ θ= °− tan cot(90 )θ θ= °− cot tan(90 )θ θ= °− sec csc(90 )θ θ= °− csc sec(90 )θ θ= °− CONCEPTS AND THEROEMS Sum of the angles in any triangle is 180˚ Pythagorean Theorem: 2 2 2a b c+ = (p5) 30°-60°-90° triangle (p7) 45°-45°-90° triangle (p9) Signs of the trigonometric functions (p29) Cofunction Theorem (p56) Exact values of sine, cosine, and tangent (p58) Significant digits (p71) YOU SHOULD BE ABLE TO: Find the complement and supplement of an angle Use the Pythagorean Theorem to find the missing length of a right triangle Find the missing lengths of a 30°-60°-90° or 45°-45°-90° triangle Draw an angle in standard position and find a coterminal angle Find the six trigonometric ratios given a point P on the terminal side of θ Determine the sign of the six trigonometric ratios in each quadrant Given the value of one trigonometric ratio, find the remaining trigonometric ratios Simplify an expression or verify an identity using the x, y, r definitions Simplify an expression or verify an identity using thebasic identities (p48) Given the value of one trigonometric ratio, use the basic identities to find the remaining ratios Find the value of a trigonometric ratio (by hand) for any quadrantal angle (0°, 90°, 180°, 270°) Find the value of a trigonometric ratio (by hand) for a 30°, 60° or 45° angle Find the six trigonometric ratios given the lengths of two sides of a right triangle Convert from decimal degrees to DMS (degrees/minutes/seconds) or vice-versa by hand and using a calculator Add or subtract angle measures in DMS format by hand and using a calculator Find the value of a trigonometric ratio for a given angle using your calculator Find the angle given the value of a trigonometric ratio using your calculator (inverse keys) Solve right triangles and applications involving right triangles Add and subtract vectors geometrically Find the horizontal and vertical components of a vector given the magnitude and direction