You are given an equation of the form cos x = k wherek 2 0. cos x = 0.7 (a) Use the graph shown below to estimate (to the nearest 0.05) a root of the equation within the interval osxS T/2. 1.0 0.9- 0.8 0.7 0.6- 0. 0.4 0.3 0.2 0.1- 0.1 0.2 0.3 0.4 0.5 0.6 07 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 y = cos x, 0 SxS T/2 (b) Use a calculator to obtain a more accurate value for the root in part (a). Round the answer to four decimal places. (c) Use the reference-angle concept and a calculator to find another root of the equation (within the interval oSxS 27). Round the answer to four decimal places. (d) Use the reference-angle concept and a calculator to find all solutions of the equation cos x = -k within the interval OSXS 2n. Again, round the answers to four decimal places. (Enter your answers as a comma-separated list.)
You are given an equation of the form cos x = k wherek 2 0. cos x = 0.7 (a) Use the graph shown below to estimate (to the nearest 0.05) a root of the equation within the interval osxS T/2. 1.0 0.9- 0.8 0.7 0.6- 0. 0.4 0.3 0.2 0.1- 0.1 0.2 0.3 0.4 0.5 0.6 07 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 y = cos x, 0 SxS T/2 (b) Use a calculator to obtain a more accurate value for the root in part (a). Round the answer to four decimal places. (c) Use the reference-angle concept and a calculator to find another root of the equation (within the interval oSxS 27). Round the answer to four decimal places. (d) Use the reference-angle concept and a calculator to find all solutions of the equation cos x = -k within the interval OSXS 2n. Again, round the answers to four decimal places. (Enter your answers as a comma-separated list.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![You are given an equation of the form cos x = k where k 2 0.
cos x = 0.7
(a) Use the graph shown below to estimate (to the nearest 0.05) a root of the equation within the interval 0 sx < T/2.
y
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3 1.4 1.5
y = cos x, 0 <xS T/2
(b) Use a calculator to obtain a more accurate value for the root in part (a). Round the answer to four decimal places.
(c) Use the reference-angle concept and a calculator to find another root of the equation (within the interval 0 xS 2n). Round the answer to four decimal places.
(d) Use the reference-angle concept and a calculator to find all solutions of the equation cos x = -k within the interval 0 < x < 2n. Again, round the answers to four decimal places. (Enter your answers as a comma-separated list.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7e29160-8b58-485e-8a5b-b6eaf19fb950%2F138aacdc-da67-4389-8ed9-c43f8b9a80c7%2Fpwma34k_processed.png&w=3840&q=75)
Transcribed Image Text:You are given an equation of the form cos x = k where k 2 0.
cos x = 0.7
(a) Use the graph shown below to estimate (to the nearest 0.05) a root of the equation within the interval 0 sx < T/2.
y
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3 1.4 1.5
y = cos x, 0 <xS T/2
(b) Use a calculator to obtain a more accurate value for the root in part (a). Round the answer to four decimal places.
(c) Use the reference-angle concept and a calculator to find another root of the equation (within the interval 0 xS 2n). Round the answer to four decimal places.
(d) Use the reference-angle concept and a calculator to find all solutions of the equation cos x = -k within the interval 0 < x < 2n. Again, round the answers to four decimal places. (Enter your answers as a comma-separated list.)
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