Download exam ii review - Linn-Benton Community College

TRIGONOMETRY
EXAM II REVIEW
Read the directions carefully. I want you to SHOW YOUR WORK for each
problem. A solution, even a correct solution, will not receive full credit if there
is no support work or explanation. Partial credit is always considered, so
showing your work is to your advantage.
3.2
Arc Length and the Area of a Circular Sector
 Be able to find the arc length, the central angle (in degrees or radians), or the radius of a
circle, given the other two.
 Be able to find the area of a sector of a circle, the central angle (in degrees or radians), or
the radius of a circle, given the other two.
 Be able to solve applied problems related to arc length and the area of a sector.
3.4
Definition 3 of Trigonometric Functions: Unit Circle Approach
 Be able to use the unit circle to evaluate any trigonometric function for angles that are
multiples of (/6 or /4) and (30  or 45  ).
 Be able to use the unit circle and the fact that sine is an odd function and cosine is an
even function to evaluate any trigonometric function for negative angles that are
multiples of (/6 or /4) and (30  or 45  ).
 Be able to use the unit circle to find the measure of an angle(s), given a trigonometric
function value for the angle.
 Be able to solve applied problems involving sines and cosines when given a formula.
4.1
Basic Graphs Of Sine and Cosine Functions: Amplitude and Period
 Be able to graph one period of the standard sine and cosine functions.
 Be able to graph one period of the sine or cosine function when the amplitude is changed.
 Be able to graph one period of the sine or cosine function when it is reflected over the xaxis.
 Be able to graph one period of the sine or cosine function when the period is changed.
 Be able to graph a sine or cosine function when given an interval.
 Be able to graph one period of the sine or cosine function when any combination of
amplitude change, period change or reflection occur.
 Be able to find the amplitude, and period of a sine or cosine function, given its graph.
 Be able to find the equation of a sine or cosine function given its graph.
 Be able to solve applied problems involving finding the amplitude, period or frequency
of a sine or cosine function when given a formula.
4.2
Translations of the Sine and Cosine Functions
 Be able to graph one period of the sine or cosine function when there is a vertical shift.
 Be able to graph one period of the sine or cosine function when there is a phase shift
(horizontal shift).
 Be able to graph one period of the sine or cosine function when there is a combination of
amplitude change, period change, reflection, vertical shift, and phase shift (horizontal
shift).
 Be able to find the amplitude, period, vertical shift and phase shift of a sine or cosine
function, given its formula.
 Be able to find the amplitude, period, vertical shift and phase shift of a sine or cosine
function, given its graph.
 Be able to graph a sine or cosine function when given an interval.
 Be able to find the equation of a sine or cosine function given its graph.
4.3
Graphs of Tangent, Cotangent, Secant and Cosecant Functions
 Be able to graph one period of the standard tangent, cotangent, secant or cosecant
function.
 Be able to graph one period of the tangent, secant, cosecant or cotangent function when
the “amplitude” is changed.
 Be able to graph one period of the tangent, secant, cosecant or cotangent function when it
is reflected over the x-axis.
 Be able to graph one period of the tangent, secant, cosecant or cotangent function when
the period is changed.
 Be able to graph one period of the tangent, secant, cosecant or cotangent function when
there is a vertical shift.
 Be able to graph one period of the tangent, secant, cosecant or cotangent function when
there is a phase shift (horizontal shift).
 Be able to graph one period of the tangent, secant, cosecant or cotangent function when
there is a combination of “amplitude” change, period change, reflection, vertical shift,
and phase shift (horizontal shift).
 Be able to graph a tangent, secant, cosecant or cotangent function when given an interval.
 Be able to find the period, vertical shift and phase shift of a tangent, secant, cosecant or
cotangent function, given its formula.
5.1
Verifying Trigonometric Identities
 Be able to simplify a trigonometric expression using the identities on page 259.
 Be able to prove/verify a trigonometric identity.
Guidelines:
1. Work on the more complicated side.
2. Look for trigonometric substitutions involving the identities on page 259.
3. Use algebraic operations (Adding fractions, distributing, factoring, ...) to simplify
the expression.
4. If nothing else works, change everything to sines and cosines.
5. Peek at the other side of the identity to make sure you are heading in the right
direction.
5.2
Sum and Difference Identities
 Be able to determine the exact value of the sine, cosine, or tangent of the sum or
difference of two of our standard angles in degrees or radians.
 Be able to use the sum and difference identities to write a trigonometric expression as a
single function.
 Be able to use information about two angles and the sum and difference identities to
evaluate any of the six trigonometric functions.
 Be able to use the sum and difference identities to determine if an expression is an
identity.
5.3
Double-Angle Identities
 Be able to use a given trigonometric function value and the double angle identities to find
the exact trigonometric function value of the double angle.
 Be able to use the double angle identities to simplify and evaluate a trigonometric
expression.
 Be able to use the double angle identities to prove identities.
Chapter 3 Review (p. 174) 25 – 43 odd, 65 – 83 odd
Chapter 4 Review (p. 251) 1 – 39 odd, 45 – 53 odd, 59 – 63 odd
Chapter 5 Review (p. 313) 1 – 11 odd, 17 – 29 odd, 33 – 41 odd