QUESTION 5 i) By sketching each of the graphs y = cosec x and y = x(n - x) for 0 < x < T, show that the equation cosec x = x(n - x) has exactly two real roots in the interval 0

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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QUESTION 5
i) By sketching each of the graphs y = cosec x and y = x(T - x) for 0 < x < T, show
that the equation cosec x = x(1 - x) has exactly two real roots in the interval
0 < x < T.
ii) Show that the equation cosec x = x(n - x) can be written in the form
x = (1 + x' sin x) / n sin x.
ii) The two real roots of the equation cosec x = x(n - x) in the interval 0 < x < n are
denoted by a and ß, where a < B.
a) Use the iterative formula,
Xpa = (1 + x, sin x,) / T sin x,
to find a correct to 2 decimal places. Give the result of each iteration to 4
decimal places.
b) Deduce the value of ß correct to 2 decimal places.
Transcribed Image Text:QUESTION 5 i) By sketching each of the graphs y = cosec x and y = x(T - x) for 0 < x < T, show that the equation cosec x = x(1 - x) has exactly two real roots in the interval 0 < x < T. ii) Show that the equation cosec x = x(n - x) can be written in the form x = (1 + x' sin x) / n sin x. ii) The two real roots of the equation cosec x = x(n - x) in the interval 0 < x < n are denoted by a and ß, where a < B. a) Use the iterative formula, Xpa = (1 + x, sin x,) / T sin x, to find a correct to 2 decimal places. Give the result of each iteration to 4 decimal places. b) Deduce the value of ß correct to 2 decimal places.
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