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Review of Trigonometry

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use and recreate the unit circle to find trig values of special angles ... Practice with Trig Functions ... Solving Basic Trig Equations. Example 1. Solve the ... – PowerPoint PPT presentation

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Title: Review of Trigonometry


1
Review of Trigonometry
  • Appendix D.3

2
After this lesson, you should be able to
  • work in radian measure
  • find reference angles
  • use and recreate the unit circle to find trig
    values of special angles
  • recognize and sketch the graphs of sine, cosine
    and tangent
  • use the Pythagorean trig identities and
    reciprocal identities to simplify trig
    expressions
  • solve basic trig equations

3
Angles
initial ray ? on x-axis
acute angles? angles between 0 and ?/2 radians
obtuse angles? angles between ?/2 and ? radians
co-terminal angles? angles that share the same
terminal ray
Ex ?/2 and -3?/2
4
Measuring Angles
Positive angles? measured counterclockwise
Negative angles? measured clockwise
5
Radian Measure
Radian measure of a central angle in the unit
circle is the length of the arc of the sector.
6
Definitions of Trig Functions
Circular Function Definitions
7
Quadrant Signs for Trig Functions
Quad I All trig functions are
Quad II Sine and cosecant are
Quad III Tangent and cotangent are
Quad IV Cosine and secant are
8
Common 1st Quadrant Angles
Degrees 0 30 45 60 90
Radians
Sin ?
Cos ?
Tan ?
9
Unit Circle Function Definitions
?
1
y
?
x
r 1
Unit circle
10
Unit Circle with Special Angles
For ? a positive angle.
r 1
Remember x cos?, y sin?
11
Reciprocal Identities
12
Trigonometric Identities Formulas
Note Those written in blue should be memorized.
13
Graph of Sine
Graph the function y sin x over the interval
-2?, 2?. State its amplitude, period,domain
and range.
14
Graph of Cosine
Graph the function y cos x over the interval
-2?, 2?. State its amplitude, period,domain
and range.
15
Graph of Tangent
Graph the function y tan x over the interval
-2?, 2?. State its period,domain and range.
16
Practice with Conversions
Example Convert 850 to exact radian measure.
Example Convert -34?/15 to degree measure.
17
Practice with Trig Functions
Example Given a point on the terminal side of ?
in standard position, find the exact value of the
six trig. functions of ?.
P (-4, -3)
18
Practice with Trig Functions
Example Given the quadrant and one
trigonometric function value of ? in standard
position, find the exact value of the other five
trig. functions.
A. Quadrant I tan ? 5
19
Practice with Trig Functions
B. Quadrant III cot ? 1
20
Solving Basic Trig Equations
Example 1Solve the equation without using a
calculator.
21
Solving Basic Trig Equations
Example 2Solve the equation without using a
calculator.
22
Homework
Exercises for Appendix D.3 1-7 all, 11-19 all,
27-35 odd
Appendix D.3 can be found online at the textbook
site and also on the CD provided with your text.
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