How do you sketch the curve $y=cos^2x-sin^2x$ by finding local maximum, minimum, inflection points, asymptotes, and intercepts?

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How do you sketch the curve $y=cos^2x-sin^2x$ by finding local maximum, minimum, inflection points, asymptotes, and intercepts?

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Answer 1 · 2017-07-26T21:42:55

Note that we can use the trigonometric identity:

$cos^2x-sin^2x = cos 2x$

so we know that the function has a maximum for $x = kpi$ and a minimum for $x= pi/2+kpi$ with $k in ZZ$ .

The inflection points are coincident with the intercepts and are in $x= pi/4+kpi$ . The function is concave down in $(-pi/4+kpi, pi/4+kpi)$ with $k$ even, and concave up with $k$ odd.

Finally, the function is continuous for every $x in RR$ and has no limit for $x->+-oo$ and no asymptotes.

graph{cos(2x) [-2.5, 2.5, -1.25, 1.25]}

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How do you sketch the curve $y=cos^2x-sin^2x$ by finding local maximum, minimum, inflection points, asymptotes, and intercepts?

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How do you sketch the curve $y=cos^2x-sin^2x$ by finding local maximum, minimum, inflection points, asymptotes, and intercepts?