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
r
θ
= (
θ
in radians)
Sector Area: 2
1
2
A
r
θ
= (
θ
in radians)
IDENTITIES
sin( ) sin
θ
θ
−=− cos( ) cos
θ
θ
−= tan( ) tan
θ
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
