Domanda del libro di testo
Use a calculator to determine whether each statement is true or false. A true statement may lead to results that differ in the last decimal place due to rounding error. cos 40° = 2 cos 20°
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Ch. 2 - Acute Angles and Right Triangles
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
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TOC.tableOfContents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Capitolo 3, Problema 2.3.49
Use a calculator to evaluate each expression. cos 75°29' cos 14°31' - sin 75°29' sin 14°31'
Guida verificata passo dopo passo1
Recognize that the expression \( \cos 75^\circ 29' \cos 14^\circ 31' - \sin 75^\circ 29' \sin 14^\circ 31' \) matches the cosine addition formula: \( \cos A \cos B - \sin A \sin B = \cos (A + B) \).
Rewrite the expression using the formula as \( \cos (75^\circ 29' + 14^\circ 31') \).
Add the angles: \( 75^\circ 29' + 14^\circ 31' \) by adding degrees and minutes separately.
Convert the resulting angle into decimal degrees if necessary for calculator input, remembering that 1 minute = \( \frac{1}{60} \) degrees.
Use a calculator to find \( \cos \) of the sum angle obtained in the previous step.
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Angle Measurement in Degrees and Minutes
Angles can be expressed in degrees (°) and minutes ('). One degree equals 60 minutes, so to work with these angles in calculations, convert minutes to decimal degrees by dividing by 60. For example, 75°29' equals 75 + 29/60 degrees.
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Percorso guidato
5:31
Reference Angles on the Unit Circle
Cosine of Sum of Angles Formula
The expression cos A cos B - sin A sin B is the cosine of the sum of two angles, i.e., cos(A + B). This identity allows simplification of the given expression by recognizing it as cos(75°29' + 14°31').
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Percorso guidato
2:25Verifying Identities with Sum and Difference Formulas
Using a Calculator for Trigonometric Values
Calculators can evaluate trigonometric functions when angles are in decimal degrees. After converting angles from degrees and minutes to decimal form, input the sum into the cosine function to find the numerical value accurately.
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Percorso guidato
4:45How to Use a Calculator for Trig Functions
Pratica correlata
Domanda del libro di testo
Use a calculator to approximate the value of each expression. Give answers to six decimal places. In Exercises 21–28, simplify the expression before using the calculator. See Example 1.
1/csc(90°-51°)
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Domanda del libro di testo
Solve each problem. See Examples 1 and 2. Distance between Two Ships A ship leaves its home port and sails on a bearing of S 61°50'. Another ship leaves the same port at the same time and sails on a bearing of N 28°10'E. If the first ship sails at 24.0 mph and the second sails at 28.0 mph, find the distance between the two ships after 4 hr.
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Domanda del libro di testo
Use a calculator to evaluate each expression. sin 35° cos 55° + cos 35° sin 55°
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Domanda del libro di testo
Use a calculator to determine whether each statement is true or false. A true statement may lead to results that differ in the last decimal place due to rounding error. ½ sin 40° = sin [½ (40°)]
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Domanda del libro di testo
Solve each problem. See Examples 1 and 2. Flying Distance The bearing from A to C is N 64° W. The bearing from A to B is S 82° W. The bearing from B to C is N 26° E. A plane flying at 350 mph takes 1.8 hr to go from A to B. Find the distance from B to C.
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