TRIGONOMETRY
FINAL EXAM 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.
5.4
Half-Angle Formulas
 Be able to use known trigonometric function value(s) and the half angle formulas to find
the exact trigonometric function value of the half angle for sine, cosine and tangent.
 Be able to use given trigonometric function value(s) and the half angle formulas to find
the exact trigonometric function value of the half angle for sine, cosine and tangent.
 Be able to use the half angle formulas to prove identities.
6.1
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, in both degrees and radians.
 Be able to find the approximate value of the inverse cosine, inverse sine and inverse
tangent of a value using a calculator, in both degrees and radians.
 Be able to find the exact value (without a calculator) of the combination of a trigonometric
function and an inverse trigonometric function (You may want to draw a triangle to assist
you.
6.2
Solving Trigonometric Equations that involve only one Trigonometric Function
 Be able to find the exact solution(s), in degrees or radians, for a trigonometric equation
on a given interval.
 Be able to find the approximate solution(s), in degrees or radians, for a trigonometric
equation on a given interval.
 Be able to find all exact solution(s), in degrees or radians, for a trigonometric equation.
 Be able to find all approximate solution(s), in degrees or radians, for a trigonometric
equation.
 Be able to use factoring or the quadratic formula to find solution(s), in degrees or radians,
for a trigonometric equation.
6.3
Solving Trigonometric Equations that involve multiple Trigonometric Functions
 Be able to find the exact solution(s), in degrees or radians, for a trigonometric equation
by converting the equation to a single trigonometric function using trigonometric
identities.
 Be able to find approximate solution(s), in degrees or radians, for a trigonometric
equation by converting the equation to a single trigonometric function using
trigonometric identities.
7.1
Oblique Triangles and the Law of Sines
 Be able to use the Law of Sines to solve for a particular side or particular angle in a
triangle given either two angles and one side or two sides and the angle opposite one of
the given sides.
 Be able to use the Law of Sines to solve for all the sides and all of the angles in a triangle
given either two angles and one side or two sides and the angle opposite one of the given
sides.
 Be able to determine whether the ambiguous case results in 0, 1 or 2 triangles, given two
sides and the angle opposite one of the given sides.
 Be able to use the Law of Sines, in the ambiguous case, to solve for all the sides and
angles for the resulting triangle(s), if possible, given two sides and the angle opposite one
of the given sides.
 Be able to use the Law of Sines to solve applied problems.
7.2
The Law of Cosines
 Be able to use the Law of Cosines to solve for a particular side or particular angle in a
triangle given either two sides and the included angle or three sides.
 Be able to use the Law of Cosines to solve for all the sides and all of the angles in a
triangle given either two sides and the included angle or three sides.
 Be able to use the Law of Cosines to solve applied problems.
7.4
Vectors
 Be able to find the component form and magnitude of a vector, given an initial and
terminal point.
 Be able to find the magnitude and direction for a vector when given the vector in
component form.
 Be able to perform vector operations given two or more vectors.
 Be able to find the magnitude of the vertical and horizontal components of a vector given
its magnitude and direction.
 Be able to find a unit vector in the direction of a given vector
 Be able to write a vector in terms of the vectors i and j.
 Be able to solve applied problems (involving navigation, velocity, distance, and force)
using vectors.
 Be able to find the resultant of two vectors.
7.5
The Dot Product
 Be able to find the dot product of two vectors.
 Be able to find the angle between two vectors.
 Be able to determine if two vectors are orthogonal.
 Be able to use the dot product to solve work problems.
8.4
Polar Equations and Graphs
 Be able to plot points given in polar coordinates.
 Be able to convert a point from rectangular coordinates to polar coordinates.
 Be able to convert a point from polar coordinates to rectangular coordinates.
 Be able to convert an equation from rectangular coordinates to polar coordinates.
 Be able to convert an equation from polar coordinates to rectangular coordinates.
 Be able graph a polar equation by plotting points.
 Be able to use a calculator to plot polar equations, including cardioids, limacons, roses
and lemniscates.
 Be able to convert an equation from polar coordinates to rectangular coordinates and
graph the equation.
B.2 to B.4
 Be able to graph ellipses and hyperbolas given their equations.
 Be able to find the equation of an ellipse or hyperbola, given information about it (such
as center, foci, vertices length of major/minor axis, or point(s) on the curve).
 Be able to find the center, foci, vertices, length of major/minor axis for a conic section,
given its equation.
REVIEW PROBLEMS:
Chapter 5 Test (p. 313) 49 – 57 odd
Chapter 6 Test (p. 366) 1 – 19 odd, 23, 25, 27, 31, 33, 35, 39, 43, 47 – 61 odd
Chapter 7 Test (p. 433) 1 – 41 odd, 53 – 95 odd
Chapter 8 Test (p. 499) 59 – 73 odd
B.2 to B.4 - All assigned problems plus (p. 691) 3, 5, 11, 13, 17, 19