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 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

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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
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Measuring Angles
Positive angles? measured counterclockwise
Negative angles? measured clockwise
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Radian Measure
Radian measure of a central angle in the unit
circle is the length of the arc of the sector.
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Definitions of Trig Functions
Circular Function Definitions
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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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Common 1st Quadrant Angles
Degrees 0 30 45 60 90
Radians
Sin ?
Cos ?
Tan ?
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Unit Circle Function Definitions
?
1
y
?
x
r 1
Unit circle
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Unit Circle with Special Angles
For ? a positive angle.
r 1
Remember x cos?, y sin?
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Reciprocal Identities
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Trigonometric Identities Formulas
Note Those written in blue should be memorized.
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Graph of Sine
Graph the function y sin x over the interval
-2?, 2?. State its amplitude, period,domain
and range.
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Graph of Cosine
Graph the function y cos x over the interval
-2?, 2?. State its amplitude, period,domain
and range.
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Graph of Tangent
Graph the function y tan x over the interval
-2?, 2?. State its period,domain and range.
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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 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)
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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
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Practice with Trig Functions
B. Quadrant III cot ? 1
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Solving Basic Trig Equations
Example 1Solve the equation without using a
calculator.
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Solving Basic Trig Equations
Example 2Solve the equation without using a
calculator.
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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.