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Ch. 2 - Acute Angles and Right Triangles
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLial 12th EditionCh. 2 - Acute Angles and Right TrianglesProblema 2.3.26
Capitolo 3, Problema 2.3.26

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.
cos(90°-3.69°)

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1
Recognize that the expression involves the cosine of a difference: \(\cos(90^\circ - 3.69^\circ)\).
Recall the co-function identity in trigonometry: \(\cos(90^\circ - \theta) = \sin(\theta)\).
Apply this identity to rewrite the expression as \(\sin(3.69^\circ)\).
Use a calculator to find the sine of \(3.69^\circ\). Make sure your calculator is set to degree mode.
Round the result to six decimal places as requested.

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Complementary Angle Identity

The complementary angle identity states that cos(90° - θ) = sin(θ). This relationship allows simplification of trigonometric expressions by converting cosine of a complementary angle into sine, which can be easier to evaluate or interpret.
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3:35
Intro to Complementary & Supplementary Angles

Using a Calculator for Trigonometric Values

Calculators can compute trigonometric functions like sine and cosine, but the angle mode (degrees or radians) must be set correctly. For angles given in degrees, ensure the calculator is in degree mode to get accurate results.
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4:45
How to Use a Calculator for Trig Functions

Rounding and Decimal Precision

When approximating values, it is important to round the result to the specified number of decimal places. Here, answers should be rounded to six decimal places to maintain consistency and precision in reporting the value.
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2:22
Cardioids Example 1
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Solve each problem. See Examples 1 and 2. Distance between Two Cities The bearing from Atlanta to Macon is S 27° E, and the bearing from Macon to Augusta is N 63° E. An automobile traveling at 62 mph needs 1¼ hr to go from Atlanta to Macon and 1¾ hr to go from Macon to Augusta. Find the distance from Atlanta to Augusta.

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Concept Check The two methods of expressing bearing can be interpreted using a rectangular coordinate system. Suppose that an observer for a radar station is located at the origin of a coordinate system. Find the bearing of an airplane located at each point. Express the bearing using both methods. (-3, -3)

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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.

cos 41° 24'

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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(30° + 20°) = cos 30° + cos 20°

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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.

sin 38° 42'

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Find two angles in the interval [0°, 360°) that satisfy each of the following. Round answers to the nearest degree. tan θ = 0.70020753

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