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.
3.3
Definition III: Circular Functions
 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 to find the measure of an angle(s), given a trigonometric
function value for the angle.
 Be able to evaluate any trigonometric function for an angle given a point on unit circle
that is on the terminal side of the angle.
 Be able to identify the domain and range for each of the six trigonometric functions.
 Be able to evaluate a trigonometric function and identify the function name, argument
and function value.
 Be able to identify how the value of a trigonometric function varies as the angle changes.
3.4
Arc Length and the Area of a Sector (Extra Credit)
 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.
3.5
Velocities (Extra Credit)
 Be able to find the linear velocity, angular velocity, or the distance traveled by an object
in a certain amount of time, given information about the other two.
 Be able to solve applied problems related to linear velocity, angular velocity, and
distance.
4.1
Basic Graphs
 Be able to graph one period of any of the six trigonometric functions (sine, cosine,
tangent, secant, cosecant, and cotangent).
 Be able to use a graph of a trigonometric function to determine the angle at which the
function takes on a particular value.
 Be able to use information about whether a trigonometric function is even or odd to
determine values of the function for negative angle values.
 Be able to use information about whether a trigonometric function is even or odd to
prove identities.
4.2
Amplitude, Reflection and Period
 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 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.
4.3
Vertical Translation and Phase Shift
 Be able to graph one period of the sine or cosine function when there is a vertical
translation.
 Be able to graph one period of the sine or cosine function when there is a phase shift
(horizontal translation).
 Be able to graph one period of the sine or cosine function when there is a combination of
amplitude change, period change, reflection, vertical translation, and phase shift
(horizontal translation).
 Be able to find the amplitude, period, vertical translation and phase shift of a sine or
cosine function, given its formula.
4.4
The Other Trigonometric Functions
 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 translation.
 Be able to graph one period of the tangent, secant, cosecant or cotangent function when
there is a phase shift (horizontal translation).
 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 translation,
and phase shift (horizontal translation).
4.5
Finding an Equation from Its Graph
 Be able to find the equation of a sine or cosine function, given its graph which may
include a combination of amplitude change, period change, reflection, vertical translation,
and phase shift (horizontal translation).
 Be able to find the equation of sine or cosine function in an applied problem setting.
4.7
Inverse Trigonometric Functions
 Be able to find the exact value (without a calculator) of the inverse cosine, inverse sine or
inverse tangent for our standard trigonometric values.
 Be able to find the approximate value of the inverse cosine, inverse sine and inverse
tangent of a value using a calculator.
 Be able to find the exact value (without a calculator) of the combination of a trigonometric
function and an inverse trigonometric function.
5.1
Proving Identities
 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 257.
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 the right
directions.
5.2
Sum and Difference Formulas
 Be able to determine the exact value of the sine, cosine, or tangent of the sum or
difference of two of our standard angles.
 Be able to use the sum and difference formulas to prove identities.
 Be able to use the sum and difference formulas to write a trigonometric expression as a
single function.
 Be able to use the sum and difference formulas to graph a trigonometric expression.
 Be able to use information about two angles and the sum and difference formulas to
evaluate any of the six trigonometric functions.
5.3
Double-Angle Formulas
 Be able to use a given trigonometric function value and the double angle formulas to find
the exact trigonometric function value of the double angle.
 Be able to use the double angle formulas to graph a trigonometric expression.
 Be able to use the double angle formulas to prove identities.
5.4
Half-Angle Formulas
 Be able to use a given (or known) trigonometric function value(s) and the half angle
formulas to find the exact trigonometric function value of the half angle.
 Be able to use the half angle formulas to graph a trigonometric expression.
 Be able to use the half angle formulas to prove identities.
Chapter 3 Test (p. 164) 12 - 18, (19 - 28 EC)
Chapter 4 Test (p. 252) 1 - 4, 6 - 19, 22 - 30
Chapter 5 Test (p. 296) 1 - 10, 13- 22