Trigonometry Final Exam Study Guide

General Study Tips: •rework all tests and take-home quizzes, example problems from class, and tests in online test archive •memorize formulas and names of formulas, and the cases to which you apply them

Topics to Know: Algebra •manipulate fractions, including complex fractions •rationalize denominators •factor •apply the square root theorem, zero product property, and quadratic formula Basic Trig Topics (Ch. 5): • evaluate without a calculator all six trig functions of any angle in radians or degrees having a 0, 30, 45, 60, or 90 reference angle •evaluate without a calculator all six trig functions of any angle, given one of the six trig function values and the quadrant •apply concepts of cofunction and like reference angles to evaluate trig functions given angles that are complements or have the same reference angle but are in different quadrants •convert between radians and degrees •angles of elevation and depression •linear speed, angular speed, and arc length Graphing: •graph all 6 basic trig functions • find amplitude and period •rewrite all equations by factoring to find horizontal shift (-c/b) •apply horizontal and vertical shifts •graph sum and difference of basic trig and linear functions Identities (Ch. 6): •evaluate trig functions of a given angle using sum, difference, half, and double angle identities •simplify expressions using identities •evaluate double, half, sum, and difference identities of an angle, given trig functions of one or more original angles and the quadrant(s) •evaluate inverse trig functions and compositions of inverse functions •solve trig equations for both all real values of the variable and for all values of the variable in a given interval •prove trigonometric identities Solving Triangles (Ch. 7) •identify type of triangle (SSS,SAS,SSA,ASA,AAS) •solve any triangle given at least one side and two other measures •solve word problems involving the Law of Sines and Law of Cosines •find the area of any triangle Vectors (Ch. 7) •perform arithmetic operations with vectors (scalar multiplication and vector addition/subtraction) •find the magnitude and direction angle of any vector •write vectors in component form and in terms of and •find a unit vector in the direction of any vector •find the dot product of two given vectors •find the angle between two vectors •solve word problems involving a mass on an incline •solve word problems involving heading of boats and airplanes Trigonometric Form of Complex Numbers (Ch. 7) •convert between standard form and trigonometric form •determine the modulus and argument of a given complex number •multiply and divide complex numbers in trigonometric form

Trig Functions of an Acute Angle

Converting Between Degree & Radian Measure To convert from degree to radian measure, multiply by To convert from radian to degree measure, multiply by

Arc Length and Angular Speed Variables Formulas Dimensional analysis conversion factors Example problem: A car travels at 60 miles per hour. Its wheels have a 24-inch diameter. What is the angular speed of a point on the rim of a wheel in revolutions per minute? Solution: , , Equation relating these variables:

Reciprocal Identities , , , , Sum and Difference Identities ,

Double-Angle Identities Ratio Identities

Pythagorean Identities , , , Half-Angle Identities , Cofunction Identities

Solving Triangles Law of Sines or Law of Cosines Area of a Triangle

Vectors The component form of with and is The magnitude of a vector with component form is The reference angle for the direction angle of the vector is given by . Figure out which quadrant this angle should be in and measure the angle counterclockwise from the positive x-axis. The horizontal component of the vector is The vertical component of the vector is For a real number and a vector , the scalar product of and is . The vector is a scalar multiple of the vector . Vector Addition/Subtraction: If and , then . If is a vector and , then is a unit vector (vector with magnitude 1) in the direction of . The dot product of two vectors and is . If is the angle between two nonzero vectors and , then . Trigonometric Form of Complex Numbers A complex number , where can be written in trigonometric form as or , where is the modulus of and direction angle is referred to as the argument.