Outline for Math 119-Test 3
Date: Monday, June 22, 2009

The format of test 3 will be open questions (ie: not mult. choice or t/f). Partial credit may be awarded if the work shown warrants it. You will be required to show all of your work in order to receive full credit for a solution. You may use a calculator (not the TI 89 or TI92). You may not use any notes, books, etc.

Disclaimer: The fact that a certain specific type of problem is not named below does not preclude it from being covered on the test. This document is intended to give you an outline of the most important topics that have been covered.

• know the terminology involved in defining an angle (initial side, terminal side, vertex, standard position, positive vs negative angles, coterminal)
• know the definition of a radian in terms of arclength and radius of a circle
• know the location of angles (both in radian and degree measure) and be able to sketch angles in standard position; pay special attention to the major angles and their location in standard position
  
• be able to find coterminal, completmentary and supplementary angles of a given angle
• be able to convert from degrees to radians and vice versa
• know the formulas for arclength and area of a section and be able to use them in application problems
  

• know the points on the unit circle that are associated with each real number (angle measure)
• be able to use these points to evaluate the trig functions exactly at the major angles
  
• know the unit circle definitions of the trig functions
• know the domain, period, and symmetry properties of sine and cosine functions and be a ble to use these to evaluate trig fcns
  
• be able to use your calculator to evaluate any trig function value (in either degrees or radians)
  

• know the definitions of each of the trig functions (for acute angles) using right triangles and be able to evaluate the trig functions using these definitions
• know the two special triangles (45-45-90 and 30-60-90)
• know all of the identities stated on p. 304 and be able to use them to evaluate trig functions and to prove other identites
• be able to solve applications involving right triangles
  

• know the general definitions of the trig functions (for any angle) using a point on the terminal side of theta
• understand how the previous two sets of definitions coincide with this more general definition
• be able to use the general definitions to evaluate trig functions
• know the definition of a reference angle and be able to find the reference angle for any given angle
• be able to use reference angles together with quadrant information to find trig values of any angle
• be able to solve trig equations (like those in exercises 81-86)
  

• know the graphs of sine and cosine very well, including domain, range, intercepts, period, symmetry
• be able to find the amplitude and period of sine and cosine curves (given a formula or graph)
• be able to use the amplitude and period to sketch the graph of a sine or cosine curve
• be able to use these tools together with phase shift and your calculator to sketch graphs of sine and cosine curves
  

• know the graph of the tangent function very well, including domain, range, intercepts, asymptotes, period, symmetry
• be able to use your calculator, together with your knowledge of the other three trig functions to sketchs cotangent, secant and cosecant curves
• be able to find domain, range, intercepts asymptotes, period and symmetry for all six trig functions; several of these rely on your ability to solve trig equations (like sin x =0, etc)
  

Section 4.7: Inverse Trigonometric Functions

• know the definitions of the three inverse trig functions defined in class including domain, range and graphs (see handout for details)
  
• know the inverse properties of trig functions (see handout for details)
  
• know how to use your calculator to evaluate inv trig functions
• be able to solve problems like those on the handout

• be able to work applications that involve solving a right triangle
  

• memorize verbatim the following Fundamental Trigonometric Identities listed on p. 374:
• Reciprocal Identities
• Quotient Identities
• Pythagorean Identities
• Even/Odd Identities
  
• be able to use these identities to evaluate trig functions and performing simplifications and algebraic manipulations with trig functions
  
• be able to use the Cofunction Identities (they will be included on a formula sheet)
• be able to use all of these identities to verify other trig identites
• be sure that you start from one side and result in the other (i.e.: do not assume the identity is true and work both sides!)
  

• know the various techniques/strategies for solving trig equations;  ultimately, the goal is always to get "trig function=constant" which you can solve either exactly using major angles or approximately using inverse trig functions and your calculator
• types of equations/techniques/strategies include:
• collecting like terms
• taking square root of both sides (don't forget +/-)
• factoring
• recognizing an equation of quadratic type
• creating an equation of quadratic type by squaring both sides (will likely introduce extraneous solutions: you must check your answers!)
• using trig identities to write in terms of a single trig function
• using inverse functions
• functions of multiple angles
  
• pay attention to the directions given!!  "estimate vs exact"; "find all solutions vs solve in [0, 2pi]" etc

• see the class handout for the list of formulas that you must be able to use to solve problems as well as example problems
• you will receive a formula sheet with the exam that includes these formulas

Additional Problems
Chapter 4 Review pp. 365-368:  #3-20, 23-52, 57-63, 65-97, 99-101, 109-134, 138-144
Chapter 5 Review pp 420-422: #1-23, 25-54, 59-68, 71, 75-77, 79-81, 83-90

Good Luck!