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Unformatted text preview: MHF 4U0 Name: 6.7 Rates of Change in Trigonometric Functions
(1) Average Rate of Change Average Rate of Change = f ( x 2 ) − f ( x1 )
x 2 − x1 (2) Instantaneous Rate of Change Instantaneous Rate of Change = f (a + h ) − f (a )
h 1
π Example #1: Consider the trigonometric function y = −3 sin x − .
2
3 5 (a) Sketch one cycle of the function. 4
3
2 (b) Determine an interval where the avg. rate of change is:
(i) positive
(ii) negative
(iii) zero 1 1
2
3 (c) Determine a point where the inst. rate of change is:
(i) positive
(ii) negative
(iii) zero (d) Calculate the average rate of change for 4
5 π
3π
≤x≤
.
2
2 (e) Describe how the instantaneous rate of change varies over the interval [0, 4 ]. pg. 1/2 MHF 4U0 Name: Example #2: The position of a particle as it moves horizontally is described by the equation
πt
s(t ) = 12 sin
+ 15 , where s is the displacement, in metres, and t is the time, in seconds.
90
(a) Calculate the average rate of change of s(t) for the following intervals:
(i) 5 s to 10 s (ii) 9 s to 10 s (b) Estimate the instantaneous rate of change of s(t) at t = 10s. (c) What physical quantity does this instantaneous rate of change represent? Assigned Work: page 369 #1, 2, 4ad, 6, 7a, 9, 11, 12, 14, 15 pg. 2/2 ...
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This note was uploaded on 01/14/2012 for the course MAT 107 taught by Professor Sda during the Spring '11 term at Beacon FL.
 Spring '11
 sda
 Rate Of Change

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