Calculators and Trigonometric Functions of an Acute Angle

1
Calculators and Trigonometric Functions of an
Acute Angle

• Trigonometry
• MATH 103
• S. Rook

2
Overview

• Section 2.2 in the textbook
• Introduction to minutes and seconds
• Conversion between degrees minutes and decimal
  degrees
• Trigonometric functions and acute angles

3
Introduction to Minutes and Seconds
4
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

6
Introduction to Minutes (Example)

• Ex 1 Perform the indicated operation
• a) (63 38) (24 52)
• b) 180 (112 19)
• c) (89 38) (28 58)

7
Conversion Between Degrees Minutes and Decimal
Degrees
8
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

9
Converting from Decimal Degrees to Degrees and
Minutes (Example)

• Ex 2 Convert to degrees and minutes
• a) 63.2
• b) 96.95

10
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

11
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
13
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 calculators manual if necessary

14
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 ? if 0 lt ? lt 90 approximate the
  answer
• a) cos ? 0.5490
• b) csc ? 1.4293
• c) cot ? 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)