Textbook Question
Convert each radian measure to degrees. Write answers to the nearest minute. See Example 2(c).
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Ch. 3 - Radian Measure and The Unit Circle
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Chapter 4, Problem 62
Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.
cos s = 0.7826
Verified step by step guidance1
Identify the problem: We need to find the value of \( s \) in the interval \( [0, \frac{\pi}{2}] \) such that \( \cos s = 0.7826 \).
Recall the inverse cosine function: To find \( s \), we use the inverse cosine (arccos) function, which gives \( s = \arccos(0.7826) \).
Apply the inverse cosine: Use a calculator or a computational tool to find \( s = \arccos(0.7826) \). Make sure your calculator is set to radians since the interval is given in radians.
Round the result: After calculating \( s \), round the value to four decimal places as requested.
Verify the solution: Check that the value of \( s \) lies within the interval \( [0, \frac{\pi}{2}] \) and that \( \cos s \) is approximately 0.7826 to confirm correctness.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Inverse Trigonometric Functions
Inverse trigonometric functions allow us to find the angle when the value of a trigonometric ratio is known. For example, to find s such that cos s = 0.7826, we use the arccos (cos⁻¹) function, which returns the angle whose cosine is 0.7826.
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Introduction to Inverse Trig Functions
Domain and Range of Cosine and Arccosine
The cosine function outputs values between -1 and 1 for angles in radians. Its inverse, arccos, returns angles in the range [0, π]. Since the problem restricts s to [0, π/2], the solution must lie within this interval, ensuring the angle corresponds to the first quadrant.
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4:22Domain and Range of Function Transformations
Rounding and Approximation
When calculating trigonometric values, results often need to be rounded to a specified number of decimal places. Here, the angle s must be approximated to four decimal places, which requires careful use of a calculator or software to ensure precision and accuracy.
Recommended video:
4:45How to Use a Calculator for Trig Functions
Related Practice
Textbook Question
Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.
sin s = 0.9918
Textbook Question
Convert each radian measure to degrees. Write answers to the nearest minute. See Example 2(c).
-5.01095
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Textbook Question
Find the approximate value of s, to four decimal places, in the interval [0 , π/2] that makes each statement true.
sec s = 1.0806
1
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Textbook Question
Convert each radian measure to degrees. Write answers to the nearest minute. See Example 2(c).
0.3417
Textbook Question
Work each problem. See Example 5. Arc Length A circular sector has an area of 50 in² . The radius of the circle is 5 in. What is the arc length of the sector?