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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 2.3.16
Capitolo 3, Problema 2.3.16

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.
tan 421° 30'

Guida verificata passo dopo passo
1
Convert the angle from degrees and minutes to a decimal degree format. Since 1 minute is \( \frac{1}{60} \) of a degree, calculate the decimal degrees as \( 421 + \frac{30}{60} \).
Simplify the angle by reducing it within the standard range of \(0^\circ\) to \(360^\circ\) using the formula \( \theta_{reduced} = \theta - 360k \), where \(k\) is an integer chosen so that \( \theta_{reduced} \) lies in the desired range.
Use the tangent function on the simplified angle: \( \tan(\theta_{reduced}) \).
Use a calculator to find the approximate value of \( \tan(\theta_{reduced}) \), making sure the calculator is set to degree mode.
Round the result to six decimal places as requested.

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Angle Conversion Between Degrees and Minutes

Angles given in degrees and minutes must be converted into decimal degrees before calculation. Since 1 minute equals 1/60 of a degree, 30' is converted to 0.5°, making 421° 30' equal to 421.5°. This conversion is essential for accurate input into calculators.
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Percorso guidato
5:04
Converting between Degrees & Radians

Coterminal Angles and Angle Reduction

Angles larger than 360° can be reduced by subtracting multiples of 360° to find a coterminal angle within the standard 0° to 360° range. This simplification helps in evaluating trigonometric functions more easily and avoids calculator errors.
Video consigliato:
Percorso guidato
04:46
Coterminal Angles

Using a Calculator to Find Trigonometric Values

After simplifying the angle, use a scientific calculator set to degree mode to find the tangent value. Ensure the calculator is in the correct mode and round the result to six decimal places as required for precision.
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Percorso guidato
4:45
How to Use a Calculator for Trig Functions
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