Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
Related questions
Question
![Question 2. Chun starts with numbers a, b ≥ 0 and puts them on a line. Then they draw a semi-circle with
diameter a + b, and draw a vertical line of length e as in the diagram.
C
a
b
(1) Assuming a + b is always the same number (but a and b can change), what is the smallest possible value
of c you can get? What happens to a and b when that happens? What is the largest possible value of c
you can get (as a function of a and b)? What relationship do a and b have when that happens?
(2) Using geometry, show that c² = ab. (Hint: You may use the fact that the angle a in the diagram is always
90 degrees.)
(3) Based on your work from parts 1 and 2 you have just proved a very important inequality. Write down that
inequality.
Dear Expert:
Please just answer Part 3 and do not include Parts 1 and 2
if against policy](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F57b2446c-db64-45a7-adc5-d7c70ead2244%2F3d587345-3fa3-4948-a40a-451bc853f9c8%2Ftnst62_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 2. Chun starts with numbers a, b ≥ 0 and puts them on a line. Then they draw a semi-circle with
diameter a + b, and draw a vertical line of length e as in the diagram.
C
a
b
(1) Assuming a + b is always the same number (but a and b can change), what is the smallest possible value
of c you can get? What happens to a and b when that happens? What is the largest possible value of c
you can get (as a function of a and b)? What relationship do a and b have when that happens?
(2) Using geometry, show that c² = ab. (Hint: You may use the fact that the angle a in the diagram is always
90 degrees.)
(3) Based on your work from parts 1 and 2 you have just proved a very important inequality. Write down that
inequality.
Dear Expert:
Please just answer Part 3 and do not include Parts 1 and 2
if against policy
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