Download 2.2 - James Bac Dang

2.2 Calculators and Trigonometric Functions
of an Acute Angle
- Calculators are capable of finding
trigonometric function values.
- When evaluating trigonometric
functions of angles given in degrees,
remember that the calculator must be set
in degree mode.
- Remember that most calculator values
of trigonometric functions are
approximations.
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Example: Finding Function Values with a Calculator
• a) sin 38 24
• Convert 38 24 to decimal
degrees.
• 38 24  38 24  38.4
60
sin 38 24  sin 38.4
 .6211477
• b) cot 68.4832 
• Use the identity
1
cot  
.
tan 
• cot 68.4832 
 .3942492
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Angle Measures Using a Calculator
• Graphing calculators have three inverse
functions.
• If x is an appropriate number, then sin 1 x,cos 1 x,
or tan -1 x gives the measure of an angle whose
sine, cosine, or tangent is x.
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Example: Using Inverse Trigonometric Functions
to Find Angles
•
Use a calculator to find an angle  in the
interval [0 ,90 ] that satisfies each condition.
• sin   .8535508
Using the degree mode and the inverse sine
function, we find that an angle  having sine
value .8535508 is 58.6 .
We write the result as sin 1 .8535508  58.6
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Significant Digits for Angles (p. 70)
• A significant digit is a digit obtained by actual measurement.
• Your answer is no more accurate then the least accurate
number in your calculation.
Number of
Significant Digits
Angle Measure to Nearest:
2
3
4
Nearest degree
5
Nearest tenth of a minute, or thousandth of
a degree
Nearest ten minutes, or tenth of a degree
Nearest minute, or hundredth of a degree
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2.3 Solving Right Triangles
• Solve right triangle ABC, if A = 42 30' and c = 18.4.
B
• B = 90  42 30'
c = 18.4
B = 47 30'
a
sin A 
c
a
sin 42 30' 
18.4
a  18.4sin 42o30'
a  18.4(.675590207)
o
a  12.43
4230'
C
A
b
cos A 
c
b
18.4
b  18.4cos 42o30'
b  13.57
cos 42o30' 
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Example: Solving a Right Triangle Given Two Sides
• Solve right triangle ABC if a = 11.47 cm and c = 27.82 cm.
side opposite
sin A 
hypotenuse
11.47

 .412293314
27.82
sin 1 A  24.35
• B = 90  24.35
B = 65.65
B
a = 11.47
c = 27.82
C
A
b2  c 2  a 2
b 2  27.822  11.47 2
b  25.35
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•
•
•
•
•
Example 1: page 71
Example 2: page 71
Example 3: page 72
Example 4: page 73
Example 5: page 73
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