Transcript Angles, Degrees, and Special Triangles

Calculators and Trigonometric
Functions of an Acute Angle
Trigonometry
MATH 103
S. Rook
Overview
• Section 2.2 in the textbook:
– Introduction to minutes and seconds
– Conversion between degrees & minutes and
decimal degrees
– Trigonometric functions and acute angles
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Introduction to Minutes and
Seconds
Introduction to Minutes
• Some applications exist where angle
measurement must be more precise than
degrees
• Degrees can be broken down further into
minutes:
– 1 degree is the same as 60 minutes
• 1° = 60’
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Introduction to Minutes
(Continued)
• When adding two quantities involving degrees
and minutes:
– Carrying may be required
• The number of minutes can only be between 0 and 59
inclusive
• When subtracting two quantities involving
degrees and minutes:
– Borrowing may be required
• Recall that 1° = 60’
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Introduction to Minutes (Example)
Ex 1: Perform the indicated operation:
a) (63° 38’) + (24° 52’)
b) 180° – (112° 19’)
c) (89° 38’) – (28° 58’)
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Conversion Between Degrees &
Minutes and Decimal Degrees
Converting from Decimal Degrees
to Degrees and Minutes
• To convert from decimal degrees to degrees
and minutes:
– Use the decimal portion of the angle
– Multiply by the appropriate conversion ratio
• Align the units in the ratio so the degrees will divide
out, leaving the minutes
• 1° = 60’
8
Converting from Decimal Degrees
to Degrees and Minutes (Example)
Ex 2: Convert to degrees and minutes:
a) 63.2°
b) 96.95°
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Converting from Degrees and
Minutes to Decimal Degrees
• To convert from degrees and minutes to
decimal degrees:
– Use the minutes from the angle measurement
– Multiply by the appropriate conversion ratio
• Align the units in the ratio so the minutes will divide
out, leaving the degrees
• 1° = 60’
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Converting from Degrees and Minutes
to Decimal Degrees (Example)
Ex 3: Convert to decimal degrees – approximate
if necessary:
a) 78° 21’
b) 102° 37’
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Trigonometric Functions and
Acute Angles
Trigonometric Functions and the
Calculator
• Most angles evaluated into a trigonometric function will
not provide exact values like 0°, 30°, 45°, 60°, or 90°
• Scientific and graphing calculators should have buttons for
sin, cos, and tan
– Depending on your calculator, you may need to press sin
and then the angle OR you may need to enter the angle
and then press sin
• Calculators work in two modes – degrees and radians
– Until Chapter 3, make sure your calculator is set to degree
mode! ALL your answers will be wrong if you fail to do
this!!!!
• Consult your calculator’s manual if necessary
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Trigonometric Functions and the
Calculator (Example)
Ex 4: Use a calculator to find each of the
following – approximate the answer:
a) tan 81.43°
b) sec 71° 48’
c) csc 12.21°
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Inverse Trigonometric Functions
and the Calculator
• Sometimes we are given the value of the
trigonometric function and need to know the
measure of the acute angle
• The sin-1, cos-1, or tan-1 buttons on the
calculator will accomplish this task
– These are called the Inverse Trigonometric
Functions and we will cover them in depth later
– On some calculators, the buttons are named
arcsin, arccos, and arctan
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Inverse Trigonometric Functions
and the Calculator (Example)
Ex 5: Find θ if 0° < θ < 90° – approximate the
answer:
a) cos θ = 0.5490
b) csc θ = 1.4293
c) cot θ = 0.4827
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Summary
• After studying these slides, you should be able to:
– State how many minutes are in a degree
– Convert from decimal degrees to degrees & minutes and
vice versa
– Use a calculator to evaluate trigonometric function with a
given angle
– Use a calculator to find an acute angle given the value of
the trigonometric function
• Additional Practice
– See the list of suggested problems for 2.2
• Next lesson
– Solving Right Triangles (Section 2.3)
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