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 2

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’ 4

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’ 5

Introduction to Minutes (Example) Ex 1: Perform the indicated operation: a) (63° 38’) + (24° 52’) b)180° – (112° 19’) c)(89° 38’) – (28° 58’) 6

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° 9

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’ 10

Converting from Degrees and Minutes to Decimal Degrees (Example) Ex 3: Convert to decimal degrees – approximate if necessary: a)78° 21’ b)102° 37’ 11

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 13

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° 14

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 15

Inverse Trigonometric Functions and the Calculator (Example) Ex 5: Find θ if 0° < θ < 90° – approximate the answer: a)cos θ = b)csc θ = c)cot θ =

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) 17