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 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 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
Finding Angle Measures Using Geometry
 Be able to determine the value of vertical, alternate interior, alternate exterior, and
corresponding angles.
 Be able to identify acute, right, obtuse and scalene triangles.
 Be able to use similar triangles to calculate triangle side lengths.
 Be able to solve applied problems using similar triangles.
1.3
Definition 1 of Trigonometric Functions: Right Triangle Ratios
 Be able to use the values of a, b, and c to find the six trigonometric functions values of an
angle.
 Be able to use co-function identities to evaluate trigonometric function values.
 Be able solve applied right triangle problems when given information related to an acute
angle of the triangle.
 Be able to find the six trigonometric functions values for the angles 30  , 45  , and 60  .
1.4
Evaluating Trigonometric Functions: Exactly and with Calculators
 Be able to find the six trigonometric functions values for the angles 30  , 45  , and 60  .
 Be able to use a calculator to calculate the trigonometric function value for any acute
angle.
 Be able to add and subtract angles written in degree, minute and second form.
 Be able to convert an angle from degree, minute and second form to decimal degrees, and
from decimal degrees to degree, minute and second form
 Be able to use a calculator to calculate the trigonometric function value for any acute
angle given in degree, minute and second form or in decimal degrees.
1.5
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 applied problems involving right triangles when given one side length
and one angle measure, or two side lengths.
 Be able to solve applied right triangle problems involving angle of elevation; angle of
depression; bearing; or any other geometric description.
2.1
Angles in the Cartesian Plane
 Be able to graph any angle in standard position.
 Be able to determine in which quadrant that the terminal side in standard position lies.
 Be able to find an angle that is co-terminal to a given angle.
 Be able to find the smallest positive angle that is co-terminal to a given angle.
 Be able to solve applied problems involving co-terminal angles.
2.2
Definition 2 of Trigonometric Functions: The Cartesian Plane
 Be able to use the values of x, y, and r to find the six trigonometric functions values of an
angle.
 Be able to evaluate the six trigonometric functions for an angle, given a point on the
terminal side of the angle in standard position.
 Be able to evaluate the six trigonometric functions for an angle, given a line on which the
terminal side of the angle lies.
 Be able to evaluate the six trigonometric function values for any multiple of a 30  , 45  ,
60  or 90  angle.
 Be able to solve applied right triangle problems involving 30  , 45  , 60  or 90  angles.
2.3
Evaluating Trigonometric Functions for Non-acute Angles
 Be able to find the quadrant that an angle lies in, given the sign of two of the six
trigonometric functions for the 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 reference angle for any angle given in degrees.
 Be able to evaluate the six trigonometric function values for any multiple of a 30  , 45  ,
60  or 90  angle using reference angles.
 Be able to find the reference angle for any angle given in degrees.
 Be able to use a calculator to find the measure of a non-acute angle, given a trigonometric
function value for the angle.
2.4
Basic Trigonometric Identities
 Be able to use reciprocal identities to evaluate trigonometric functions.
 Be able to use quotient identities to evaluate trigonometric functions.
 Be able to use Pythagorean identities to evaluate trigonometric functions.
 Be able to use reciprocal identities, quotient 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.
 Be able to use trigonometric identities to simplify trigonometric expressions.
 Be able to simplify an expression after making a trigonometric substitution.
3.1
Radian Measure
 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 reference angle for any angle given in radians.
 Be able to find the exact value of any trigonometric function for all angles that are
multiples of /6, /4 or /3.
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.
Chapter 1 Review Exercises (p. 70) 1 – 41 odd, 47 – 83 odd, 87 – 101 odd
Chapter 2 Review Exercises (p. 124) 1 – 33 odd, 43 – 59 odd, 65 – 75 odd
Chapter 3 Review Exercises (p. 174) 1 – 43 odd, 65 – 83 odd