TRIGONOMETRY

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TRIGONOMETRY
Yvonne M. Conley, SSND Roman Catholic HS
Philadelphia, PA September 1999
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General Information
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• Trigonometry
• is the mathematics of right triangles.
• can be used to determine unknown distances that
  are not easily measured with a ruler.
• can be used to determine an unknown angle.
• there are six standard functions
• sin (sine) cos (cosine)
• tan (tangent) cot (cotangent)
• sec (secant) csc (cosecant)

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Trigonometric Functions
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opposite side
R
Y
angle of interest
q
X
adjacent side
adjacent
opposite
Y
X
cos q
sin q
R
R
hypotenuse
hypotenuse
opposite
Y
tan q
X
adjacent
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b
adjacent side
angle of interest
R
Y
X
opposite side
adjacent
opposite
Y
X
cos b
sin b
R
hypotenuse
hypotenuse
R
opposite
X
tan b
Y
adjacent
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Problem-Solving Strategy
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Draw a right triangle. Write in the data provided
including units. Write the question. Write an
equation. Solve the problem.
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Sample Problems
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b
Calculate the sin of q and the sin of b.
25.0 m
20.0 m
q
15.O m
sin q ?
sin b ?
x/r
sin b
sin q
y/r
sin q 20.0 m/ 25.0 m
sin b 15.0 m/ 25.0 m
sin q 0.800
sin b 0.600
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b
Calculate the cos of q and the cos of b.
25.0 m
20.0 m
q
15.O m
cos q ?
cos b ?
x/r
cos q
y/r
cos b
cos q 15.0 m/ 25.0 m
cos b 20.0 m/ 25.0 m
cos q 0.600
cos b 0.800
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b
Calculate the tangent of q and the tangent of b.
25.0 m
20.0 m
q
15.O m
tan q ?
tan b ?
y/x
tan q
x/y
tan b
tan q 20.0 m/ 15.0 m
tan b 15.0 m/ 20.0 m
tan q 1.33 ...
tan b 0.750
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Using the inverse of the trig. functions,
determine angle q .
b
25.0 m
20.0 m
tan-1 y/x q
tan-1 20.0m/15.0m q
q
53.1o q
15.O m
sin-1 y/r
q
cos-1 x/r q
cos-1 15.0m/25.0m q
sin-1 20.0m/25.0m q
53.1o q
53.1o q
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Using the inverse of the trig. functions,
determine angle b .
b
25.0 m
20.0 m
tan-1 x/y b
tan-1 15.0m/20.0m b
q
15.O m
36.9o b
sin-1 x/r
b
cos-1 y/r b
cos-1 20.0m/25.0m b
sin-1 15.0m/25.0m b
36.9o b
36.9o b
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Determine the length of an unknown distance x.
b
25.0 m
sin q y/r cos q x/r tan q y/x
?? m
q 30.0 o
?? m
tan q y/x
x y/ tan q
x 25.0 m/ tan 30.0 o
x 43.3 m
x 25.0 m / 0.577
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b
Calculate the tangent of q and the tangent of b.
25.0 m
20.0 m
q
15.O m
y/x
tan q
x/y
tan b
tan q 20.0 m/ 15.0 m
tan b 15.0 m/ 20.0 m
tan q 1.33 ...
tan b 0.750
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