Find the area enclosed between $y=1/2$ and $ y= \cos x $ for $x =[0,2π]$ I am a bit confused with this question because there is no area bound between these graphs and a book suggests to enclose areas using $Y$ axis which I find is a bit incorrect If I am wrong please let me know
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1What makes you say there is no area bound between the graphs? Can we see your plot? – Jam Jul 19 '19 at 11:07
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What do you mean to enclose areas using the $y$-axis? There is clearly a certain amount of area bounded by those two curves. Just plot them in an online graphing calculator and you will see. – Michael Rybkin Jul 19 '19 at 11:50
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Ok Thanks I got it – Rishabh Shetty Jul 20 '19 at 12:02
2 Answers
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Hint: Solve the equation $$\cos(x)=\frac{1}{2}$$ for $$0\le x\le 2\pi$$
Dr. Sonnhard Graubner
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Sir I solved it the same way but aren't we using the Y axis to enclose the area which isn't correct . – Rishabh Shetty Jul 19 '19 at 10:51
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If so then $$A_1=\int_{0}^{\pi/3}\cos(x)-\frac{1}{2}dx$$ – Dr. Sonnhard Graubner Jul 19 '19 at 10:54
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And $$A_2=\int_{\frac{5}{3}\pi}^{2\pi}\cos(x)-\frac{1}{2}dx$$ – Dr. Sonnhard Graubner Jul 19 '19 at 11:00
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Yes, this is true: $$A_3=\int_{\frac{\pi}{3}}^{\frac{5\pi}{3}}\frac{1}{2}-\cos(x)dx$$ – Dr. Sonnhard Graubner Jul 19 '19 at 11:18
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You may check this plot(courtesy Wolfram Alpha).
The area may be calculated by evaluating definite integrals between intervals,whose boundaries are on the solution of cos x = 1/2.
Sarthak Rout
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