Which quadrants and axes does $f (x) = {cos}^{2} x$ $f(x)=cos^2x$ pass through?

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Which quadrants and axes does $f (x) = {cos}^{2} x$ $f(x)=cos^2x$ pass through?

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Answer 1 · 2017-07-11T06:27:58

$f (x) = {cos}^{2} x$ $f(x)=cos^2x$ is always $0$ $0$ or positive and can take any value between $[0, 1]$ $[0,1]$ and it touches $x$ $x$ at $x = (2 k + 1) \frac{π}{2}$ $x=(2k+1)pi/2$ and passes only through $Q 1$ $Q1$ and $Q 2$ $Q2$

Explanation:

$cos x$ $cosx$ can take values only between $[- 1, 1]$ $[-1,1]$ , further when $x = 2 k π$ $x=2kpi$ $cos x = 1$ $cosx=1$ and when $x = (2 k + 1) π$ $x=(2k+1)pi$ $cos x = - 1$ $cosx=-1$ and at $x = (2 k + 1) \frac{π}{2}$ $x=(2k+1)pi/2$ , $cos x = 0$ $cosx=0$

$f (x) = {cos}^{2} x$ $f(x)=cos^2x$ is always $0$ $0$ or positive and can take any value between $[0, 1]$ $[0,1]$ and it touches $x$ $x$ -axis at $x = (2 k + 1) \frac{π}{2}$ $x=(2k+1)pi/2$

Hence it passes only through $Q 1$ $Q1$ and $Q 2$ $Q2$

and while it touches $x$ $x$ -axis at $x = (2 k + 1) \frac{π}{2}$ $x=(2k+1)pi/2$ , it crosses $y$ $y$ axis at $x = 0$ $x=0$

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Which quadrants and axes does $f (x) = {cos}^{2} x$ $f(x)=cos^2x$ pass through?

1 Answer

Explanation:

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