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MY NOTES ASK YOUR TEACHER The rate of change of the function f(x) = sin(x) + csc(x) is given by the expression cos(x) - csc(x) cot(x). Show that the expression for the rate of change can also be written as -cos(x) cot²(x). cos(x)-csc(x) cot(x) = cos(x) - sin(x) sin(x) = (cos(x)) sin²(x)) -csc²(x)) = (cos(x)) = (-cos(x))([ |-¹)

MY NOTES ASK YOUR TEACHER The rate of change of the function f(x) = sin(x) + csc(x) is given by the expression cos(x) - csc(x) cot(x). Show that the expression for the rate of change can also be written as -cos(x) cot²(x). cos(x)-csc(x) cot(x) = cos(x) - sin(x) sin(x) = (cos(x)) sin²(x)) -csc²(x)) = (cos(x)) = (-cos(x))([ |-¹)

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.4: Average Rate Of Change Of A Function
Problem 2E
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MY NOTES ASK YOUR TEACHER The rate of change of the function f(x) = sin(x) + csc(x) is given by the expression cos(x) - csc(x) cot(x). Show that the expression for the rate of change can also be written as -cos(x) cot²(x). cos(x)-csc(x) cot(x) = cos(x) - 1 sin(x) sin(x) = (cos(x))( sin²(x)) - csc²(x)) = (cos(x))( = (-cos(x)) -1) = -cos(x) cot²(x)
Transcribed Image Text:MY NOTES ASK YOUR TEACHER The rate of change of the function f(x) = sin(x) + csc(x) is given by the expression cos(x) - csc(x) cot(x). Show that the expression for the rate of change can also be written as -cos(x) cot²(x). cos(x)-csc(x) cot(x) = cos(x) - 1 sin(x) sin(x) = (cos(x))( sin²(x)) - csc²(x)) = (cos(x))( = (-cos(x)) -1) = -cos(x) cot²(x)
Verify the identity. 9 cos² B-9 sin² B = 18 cos² B-9 9 cos² B-9 sin² B = 9 cos² B-9(1- cos²B = 9 cos² B + 9 cos²B X = 18 cos² B-9 X 9
Transcribed Image Text:Verify the identity. 9 cos² B-9 sin² B = 18 cos² B-9 9 cos² B-9 sin² B = 9 cos² B-9(1- cos²B = 9 cos² B + 9 cos²B X = 18 cos² B-9 X 9
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