`arccos(x) = arcsec(x)` Solve the equation for x

Monday, August 3, 2015

$\displaystyle{\arccos{{\left({x}\right)}}}={a}{r}{c}{\sec{{\left({x}\right)}}}$ Solve the equation for x

The function at the left side, $\displaystyle{\arccos{{\left({x}\right)}}},$ is defined at $\displaystyle{\left[-{1},{1}\right]},$ because it is the range of $\displaystyle{\cos{{\left({x}\right)}}}.$ The function at the right side, $\displaystyle{a}{r}{c}{\sec{{\left({x}\right)}}},$ is defined at $\displaystyle{\left(-\infty,-{1}\right]}\cup{\left[{1},+\infty\right]},$ because it is the range of $\displaystyle{\sec{{\left({x}\right)}}}.$

Thus there are only two points at which both sides are defined, $\displaystyle{x}_{{1}}=-{1}$ and $\displaystyle{x}_{{2}}={1}.$ Let's check whether they are the solutions: $\displaystyle{\arccos{{\left(-{1}\right)}}}=\pi$ and $\displaystyle{a}{r}{c}{\sec{{\left(-{1}\right)}}}=\pi,$ $\displaystyle{\arccos{{\left({1}\right)}}}={0}$ and $\displaystyle{a}{r}{c}{\sec{{\left({1}\right)}}}={0}.$

Yes, they are the solutions. The answer: $\displaystyle{x}_{{1}}=-{1},$ $\displaystyle{x}_{{2}}={1}.$

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Monday, August 3, 2015

$\displaystyle{\arccos{{\left({x}\right)}}}={a}{r}{c}{\sec{{\left({x}\right)}}}$ Solve the equation for x

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Thomas Jefferson's election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?

Monday, August 3, 2015

Solve the equation for x

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Post a Comment

Thomas Jefferson&#39;s election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?

$\displaystyle{\arccos{{\left({x}\right)}}}={a}{r}{c}{\sec{{\left({x}\right)}}}$ Solve the equation for x

Thomas Jefferson's election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?