a. Use the definition of the derivative and the identity sin(a + B) = sin(a) cos(B) + cos(a) sin(B) to prove that [sin(x)]' = cos(x). %3D
a. Use the definition of the derivative and the identity sin(a + B) = sin(a) cos(B) + cos(a) sin(B) to prove that [sin(x)]' = cos(x). %3D
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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Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Question
![a. Use the definition of the derivative and the identity
sin(a + B) = sin(a) cos(8) + cos(a) sin(B) to prove that
[sin(x)]' = cos(x).
b. A man stands 35 metres from a helicopter sitting on a landing pad. The
helicopter begins rising into the air at a constant rate of 8 m/sec. At the same
time, the man begins to walk towards the landing pad at a constant rate of 1
m/sec. Determine the rate at which the distance between the man and the
helicopter is changing exactly 5 seconds after the helicopter launched.
c. A box is to be manufactured such that its length is exactly two times its width
and its volume is of a cubic metre. Assuming that the box is closed on all
1
sides, determine the smallest amount of material needed for its construction.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe87bf100-bb8c-4bf3-84c2-1c51bcfa9893%2F9ad6e8a6-8f2a-478c-b8da-57c8b3a28d29%2F91exdzf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:a. Use the definition of the derivative and the identity
sin(a + B) = sin(a) cos(8) + cos(a) sin(B) to prove that
[sin(x)]' = cos(x).
b. A man stands 35 metres from a helicopter sitting on a landing pad. The
helicopter begins rising into the air at a constant rate of 8 m/sec. At the same
time, the man begins to walk towards the landing pad at a constant rate of 1
m/sec. Determine the rate at which the distance between the man and the
helicopter is changing exactly 5 seconds after the helicopter launched.
c. A box is to be manufactured such that its length is exactly two times its width
and its volume is of a cubic metre. Assuming that the box is closed on all
1
sides, determine the smallest amount of material needed for its construction.
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