Ch. 1 - Trigonometric Functions

Lial12th EditionTrigonometryISBN: 9780136552161당신이 사용하는 게 아니라요?교과서 변경

Lial 12th Edition

Ch. 1 - Trigonometric Functions

문제 68

2장, 문제 68

Convert each angle measure to degrees, minutes, and seconds. If applicable, round to the nearest second. See Example 4(b). 174.255°

검증된 단계별 안내

Start with the given angle in decimal degrees: \(174.255^\circ\).

The whole number part is the degrees. So, the degrees are \(174^\circ\).

To find the minutes, take the decimal part \(0.255\) and multiply it by 60: \(0.255 \times 60\).

The whole number part of the result from step 3 is the minutes.

To find the seconds, take the decimal part from step 3's result and multiply it by 60 again, then round to the nearest second.

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주요 개념

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Decimal Degrees to Degrees, Minutes, and Seconds Conversion

This concept involves converting an angle expressed in decimal degrees into degrees, minutes, and seconds (D° M' S"). Degrees remain the integer part, minutes are obtained by multiplying the decimal remainder by 60, and seconds come from multiplying the new decimal remainder by 60 again. This method allows for a more precise and traditional representation of angles.

Rounding to the Nearest Second

After calculating the seconds in the D° M' S" format, rounding is applied to simplify the value to the nearest whole second. This step ensures the angle measurement is practical and easy to use, especially in fields like navigation or surveying where precision to the second is standard.

Understanding Angle Measurement Units

Degrees, minutes, and seconds are units used to measure angles, where 1 degree equals 60 minutes and 1 minute equals 60 seconds. This hierarchical structure helps express angles more precisely than decimal degrees alone, and is commonly used in trigonometry, astronomy, and geography.

관련 실천

교과서 질문

Convert each angle measure to degrees, minutes, and seconds. If applicable, round to the nearest second. -25.485°

707

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교과서 질문

Use identities to solve each of the following. Rationalize denominators when applicable. See Examples 5–7. Find csc θ , given that cot θ = ―1/2 and θ is in quadrant IV.

701

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교과서 질문

In each figure, there are two similar triangles. Find the unknown measurement. Give approximations to the nearest tenth.

664

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교과서 질문

Find the indicated function value. If it is undefined, say so. See Example 4. sin(―270°)

672

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교과서 질문

Solve each problem. Solar Eclipse on Earth The sun has a diameter of about 865,000 mi with a maximum distance from Earth's surface of about 94,500,000 mi. The moon has a smaller diameter of 2159 mi. For a total solar eclipse to occur, the moon must pass between Earth and the sun. The moon must also be close enough to Earth for the moon's umbra (shadow) to reach the surface of Earth. (Data from Karttunen, H., P. Kröger, H. Oja, M. Putannen, and K. Donners, Editors, Fundamental Astronomy, Fourth Edition, Springer-Verlag.) a. Calculate the maximum distance, to the nearest thousand miles, that the moon can be from Earth and still have a total solar eclipse occur. (Hint: Use similar triangles.)

804

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교과서 질문

Find the indicated function value. If it is undefined, say so. See Example 4. sec 180°

707

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