Review for Exam 2 – Trigonometry 111.004

3.2

• Arc length
• Area of a sector

3.3

• Understand the unit circle (figure 12 on page 109)
• Domains of trigonometric functions
• Find values of circular functions

Good review problems:

Ch. 3 Review (p 124-127) # 21, 24, 29-30, 33-38, 55-58

Ch. 3 Test (p. 128-129) # 7-15

Chapter 4

4.1

• Graphing sine and cosine functions
• Relating points on the unit circle to points on trig functions
• Determine the period, amplitude, and average value of a trig function

4.2

• Horizontal translations of sine and cosine functions
• Vertical translations of sine and cosine functions
• Know how to find a, b, c, and d (and what they represent) in the following:

y = c + a sin b(x-d) or y = c + a cos b(x-d)

4.3

• Graphing tangent function (how to find asymptotes, etc)
• Translations of the tangent function
• You will NOT be tested on secant or cosecant graphs

Good review problems:

Ch. 4 Review (p. 175-178) # 5-12, 15, 17-19, 23-25, 27-28, 31-33, 35-36, 38-42

Ch. 4 Test (p. 178) # 1, 2, 4, 5

Chapter 5

5.1

• Know and apply the Fundamental Identities (quotient and reciprocal identities)
• Know and apply Pythagorean Identities
• Know and apply Negative-Angle Identities
• Express trig functions in terms of other trig functions using identities
• Rewrite an expression only in terms of cosine and sine

5.2

• Verify trig identities
• Simplify a trig expression

5.3

• Know and apply the sum and difference identities for cosine
• Find the sum identity for cosine using the difference identity for cosine
• You do NOT have to derive the difference identity for cosine, but you do need to know it and be able to apply it
• Cofunction identities!!
• Find cos(s+t) and cos(s-t) given certain information, such as cos(s) and sin(t) and the quadrants of s and t

5.4

• Know and apply the sum and difference identities for sine

• Find the difference identity for sine using the sum identity for sine

• Find sin(s+t) and sin(s-t) given certain information, such as cos(s) and sin(t) and the quadrants of s and t
• Verify identities using sum and difference identities

5.5

• Know and apply the double-angle identities

• Be able to derive all forms of the double-angle identities
• Verify identities using double-angle identities

Good review problems:

Ch. 5 Review (p. 231-233) # 1-15, 16a, 17-26, 27-32 (not tangent), 49-64

Ch. 5 Test (p. 233-234) # 1- 3, 5, 7-11

Chapter 6

6.1

• Definitions of a function, one-to-one function, and inverse function
• Domains and ranges of inverse sine, inverse cosine, and inverse tangent functions
• Know how to graph an inverse function (reflecting over y = x line)
• Find exact values of inverse trig function expressions
• Solve functions of the form tan(arcos(3/4)), for example

6.2

• Solve trig equations that are linear and quadratic

• Apply identities in order to simplify and then solve trig equations

6.3

• Solve trig equations that contain multiple angles
• Use identities to solve trig equations with multiple angles (often apply double-angle formulas)

6.4

• Solve for x in terms of y using inverse functions

• Solve inverse trig functions

Good review problems:

Ch. 6 Review (p. 271-273) # 1-10, 14-16, 23-25, 27-30, 34-38, 41, 43-49, 51-55

Ch. 6 Test (p. 273-274) # 1, 2a-c, 3-7, 9-10