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## Review of Trigonometry

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### work in radian measure. find reference angles. use the unit circle to find trig values of special angles ... obtuse angles angles between /2 and radians ... – 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
• find reference angles
• use the unit circle to find trig values of
special angles
• recognize and sketch the graphs of sine, cosine
and tangent

3
Angles
initial ray ? on x-axis
terminal ray
acute angles? angles between 0 and ?/2 radians
initial ray
obtuse angles? angles between ?/2 and ? radians
Standard position of an angle
co-terminal angles? angles that share the same
terminating ray
Ex ?/2 and -3?/2
4
Measuring Angles
Positive angles? measured counterclockwise
Negative angles? measured clockwise
5
Radian measure is the length of the arc of the
sector.
The length of the sector
?
?
s r?
r 1
?
r
Unit circle
Arc Length is
6
Circular Function Definitions
(x,y)
r
y
?
Circular Function Definitions
x
7
Unit Circle Function Definitions
?
1
y
?
x
Unit circle
8
Trigonometric Identities Formulas
9
Reciprocal Identities
10
11
12
Unit Circle
The unit circle may be found in your text in the
front cover on a tear out reference sheet. You
should expect to memorize it.
13
Graph of Sine
Graph the function y sin x over the interval
-2?, 2?. Then, determine the domain and range.
14
Graph of Cosine
Graph the function y cos x over the interval
-2?, 2?. Then, determine the domain and range.
15
Graph of Tangent
Graph the function y tan x over the interval
-2?, 2?. Then, determine the domain and range.
16
Quad I All trig functions are
Quad II Sine and cosecant are
Quad III Tangent and cotangent are
Quad IV Cosine and secant are
17
Practice with Conversions
Example Convert 850 to exact radian measure.
Example Convert -34?/15 to degree measure.
18
Practice with Trig
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)
In which quadrant will we find P?
III
19
Practice
Example Given the quadrant and one
trigonometric function value of ? in standard
position, find the exact value of the trig.
function.
A. Quadrant I tan ? 5
B. Quadrant III cot ? 1
20
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.