Review of Trigonometry

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Review of Trigonometry

• Appendix D.3

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After this lesson, you should be able to

• work in radian measure
• find reference angles
• use the unit circle to find trig values of
  special angles
• recognize and sketch the graphs of sine, cosine
  and tangent

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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
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Measuring Angles
Positive angles? measured counterclockwise
Negative angles? measured clockwise
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Radian Measure
Radian measure is the length of the arc of the
sector.
The length of the sector
?
?
s r?
r 1
?
r
Unit circle
circle with radius r
Arc Length is
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Circular Function Definitions
(x,y)
r
y
?
Circular Function Definitions
x
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Unit Circle Function Definitions
?
1
y
?
x
Unit circle
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Trigonometric Identities Formulas
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Reciprocal Identities
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Common 1st Quadrant Angles
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Common 1st Quadrant Angles
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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.
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Graph of Sine
Graph the function y sin x over the interval
-2?, 2?. Then, determine the domain and range.
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Graph of Cosine
Graph the function y cos x over the interval
-2?, 2?. Then, determine the domain and range.
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Graph of Tangent
Graph the function y tan x over the interval
-2?, 2?. Then, determine the domain and range.
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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
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Practice with Conversions
Example Convert 850 to exact radian measure.
Example Convert -34?/15 to degree measure.
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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
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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
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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.