Skip to main content
Ch. 2 - Acute Angles and Right Triangles
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161Not the one you use?Change textbook
All textbooksLial 12th EditionCh. 2 - Acute Angles and Right TrianglesProblem 2.3.38
Chapter 3, Problem 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

Verified step by step guidance
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.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
1m
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.
Recommended video:
5:53
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.
Recommended video:
4:49
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.
Recommended video:
5:04
Converting between Degrees & Radians
Related Practice
Textbook Question

(Modeling) Fish's View of the World The figure shows a fish's view of the world above the surface of the water. (Data from Walker, J., 'The Amateur Scientist,' Scientific American.) Suppose that a light ray comes from the horizon, enters the water, and strikes the fish's eye. Assume that this ray gives a value of 90° for angle θ₁ in the formula for Snell's law. (In a practical situation, this angle would probably be a little less than 90°.) The speed of light in water is about 2.254 x 10⁸ m per sec. Find angle θ₂ to the nearest tenth.

606
views
Textbook Question

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

617
views
Textbook Question

Determine whether each statement is true or false. If false, tell why. Use a calculator for Exercises 39 and 42. 1 tan² 60° = sec² 60°

659
views
Textbook Question

Solve each problem. See Examples 3 and 4. Height of an Antenna A scanner antenna is on top of the center of a house. The angle of elevation from a point 28.0 m from the center of the house to the top of the antenna is 27°10', and the angle of elevation to the bottom of the antenna is 18°10'. Find the height of the antenna.

861
views
Textbook Question

Find two angles in the interval [0°, 360°) that satisfy each of the following. Round answers to the nearest degree. cos θ = 0.10452846

608
views
Textbook Question

Use a calculator to approximate the value of each expression. Give answers to six decimal places. tan 11.7689°

617
views