Mathematics

Problem

Between

x = 0

and

x = 2\pi

(radians) the graphs of

y = \sin x

and

y = \cos x

intersect several times and enclose more than one bounded region. a. (i) Find all

x

-coordinates in the interval

[0,2\pi]

at which the curves

y = \sin x

and

y = \cos x

intersect. b. (ii) Using these points, formulate the necessary definite integral(s) and evaluate them to obtain the total area of all regions enclosed between the two curves over

0 \le x \le 2\pi

. Give the result correct to three decimal places.

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