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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 2.3.38
Capitolo 3, Problema 2.3.38

Find a value of θ in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places. See Example 2.
cos θ = 0.85536428

Guida verificata passo dopo passo
1
Identify the given equation: \(\cos \theta = 0.85536428\) and the interval for \(\theta\) is \([0^\circ, 90^\circ)\).
Recall that the cosine function is positive and decreasing in the first quadrant, so there will be one solution for \(\theta\) in the given interval.
Use the inverse cosine function to find \(\theta\): \(\theta = \cos^{-1}(0.85536428)\).
Calculate the value of \(\theta\) using a calculator set to degree mode to get the angle in degrees.
Round the result to six decimal places as required.

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Cosine Function and Its Properties

The cosine function relates an angle in a right triangle to the ratio of the adjacent side over the hypotenuse. It is periodic and ranges between -1 and 1. Understanding its behavior on the interval [0°, 90°) is essential for finding the angle corresponding to a given cosine value.
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Graph of Sine and Cosine Function

Inverse Cosine (Arccos) Function

The inverse cosine function, denoted arccos or cos⁻¹, returns the angle whose cosine is a given number. It is used to find the angle θ when cos θ is known, typically producing results in the range [0°, 180°]. For this problem, restricting the solution to [0°, 90°) is important.
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Inverse Cosine

Decimal Degree Precision

Decimal degree precision refers to expressing angles in degrees with decimal points, allowing for more exact measurements. Here, answers must be given to six decimal places, which requires careful calculation and rounding to ensure accuracy.
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Converting between Degrees & Radians
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CONCEPT PREVIEW Match each trigonometric function value or angle in Column I with its appropriate approximation in Column II.


Column I: 1.

cot⁻¹ 30

Column II:

A. 88.09084757°

B. 63.25631605°

C. 1.909152433°

D. 17.45760312°

E. 0.2867453858

F. 1.962610506

G. 14.47751219°

H. 1.015426612

I. 1.051462224

J. 0.9925461516

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