Download exam i review - Linn-Benton Community College

TRIGONOMETRY
EXAM I 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.
1.1
Angles, Degrees and Special Triangles
 Be able to identify acute, right, obtuse and straight angles.
 Be able to find the complement and supplement of an angle.
 Be able to identify acute, right, obtuse and scalene triangles.
 Be able to solve for the length of any side of a right triangle.
 Be able to find the exact side length of any side in a 45  - 45  - 90  or 30  - 60  - 90 
triangle.
 Be able to solve applied problems related to right triangles.
1.2
The Rectangular Coordinate System
 Be able to graph a line or parabola.
 Be able to find the distance between two points.
 Be able to find the equation of a circle, given information about the circle.
 Be able to graph the unit circle and find the value of the y - coordinate of a point, given
the x - coordinate.
 Be able to find an angle that is coterminal to a given angle.
1.3
Definition I: Trigonometric Functions
 Be able to use the values of x, y, and r to find the six trigonometric functions values of an
angle.
 Be able to find the six trigonometric functions values of any angle that is a multiple of
30  or 45  (our favorite angles).
 Be able to find the sign of any of the six trigonometric functions, given an angle.
 Be able to find all trigonometric functions values for an angle, given one of the function
values and information about the quadrant that the angle lies in.
 Be able to find the quadrants that an angle lies in, given the sign of any of the six
trigonometric functions for the angle.
1.4
Introduction to Identities
 Be able to use reciprocal identities to evaluate trigonometric functions.
 Be able to use ratio identities to evaluate trigonometric functions.
 Be able to use Pythagorean identities to evaluate trigonometric functions.
 Be able to use reciprocal identities, ratio identities, and Pythagorean identities to evaluate
trigonometric functions given one of the trigonometric function values and information
about the quadrant in which the angle lies.
1.5
More on Identities
 Be able to use trigonometric identities to convert one trigonometric to function to another.
 Be able to use trigonometric identities to simplify trigonometric expressions.
 Be able to add and subtract trigonometric expressions.
 Be able to simplify an expression after making a trigonometric substitution.
 Be able to use trigonometric identities to prove another trigonometric identity.
2.1
Definition II: Right Triangle Trigonometry
 Be able to evaluate the six trigonometric functions for an angle, given two sides of a
triangle either numerically or graphically.
 Be able to evaluate the six trigonometric functions for an angle, given a graph of the angle
and a point on the terminal side, by forming a triangle.
 Be able to evaluate a trigonometric function, given information about its cofunction.
 Be able to evaluate a trigonometric expression by substituting exact values from 45  - 45 
- 90  or 30  - 60  - 90  triangles.
2.2
Calculators and Trigonometric Functions of an Acute Angle
 Be able to add and subtract angles written in degree and minute form.
 Be able to convert an angle from degree and minute form to decimal degrees, and from
decimal degrees to degree and minute form.
 Be able to use a calculator to calculate the trigonometric function value for any acute
angle.
 Be able to use a calculator to find the measure of the acute angle, given a trigonometric
function value for the angle.
2.3
Solving Right Triangles
 Be able to find any side length or angle measure of a triangle given either, one side length
and one angle measure, or two side lengths.
 Be able to find all side lengths and all angle measures of a triangle given either, one side
length and one angle measure, or two side lengths.
 Be able to solve for a given length for graphical problems involving right triangles.
2.4
Applications
 Be able to represent an angle/triangle for an applied problem involving any of the
following: angle of elevation; angle of depression; bearing; or any other geometric
description.
 Be able to solve (find lengths or angle measures) for applied problems involving right
triangles using the six trigonometric functions.
2.5
Vectors: A Geometric Approach
 Be able to determine graph a vector given its direction and magnitude.
 Be able to find the magnitude of the vertical and horizontal components of a vector given
its magnitude and direction.
 Be able to find the magnitude of a vector given the magnitude of its vertical and
horizontal components.
 Be able to solve applied problems ( involving navigation, velocity, distance, force and
work) using vectors.
3.1
Reference Angle
 Be able to find the reference angle for any angle measured in degrees.
 Be able to find the exact value of any trigonometric function for angles that are multiples
of 30  or 45  (our favorite angles).
 Be able to use a calculator to approximate the value of any trigonometric function for any
angle.
 Be able to use a calculator to find the measure of an angle, given a trigonometric function
value for the angle and the quadrant in which the angle lies.
3.2
Radians and Degrees
 Be able to find the radian angle measure given an arc length and radius.
 Be able to convert an angle from degrees to radians and from radians to degrees.
 Be able to find the exact value of any trigonometric function for all angles that are
multiples of /6 or /4.
 Be able to substitute a radian angle into a trigonometric expression and evaluate it and
write the result as an ordered pair.
Chapter 1 Test (p. 48) 1 - 7, 9 - 12, 14 - 30
Chapter 2 Test (p. 106) 1 - 3, 5 - 21, 23 - 27, 30,
Chapter 3 Test (p. 164) 1 - 13