Solve y=4x/5-tan(x) | Microsoft Math Solver

Solve for y (complex solution)

y=\frac{8ix\cos(x)}{\left(-1+5i\right)e^{ix}+\left(1+5i\right)e^{-ix}}

\nexists n_{2}\in \mathrm{Z}\text{ : }x=\pi n_{2}+\arctan(5)\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }x=\frac{\pi \left(2n_{1}+1\right)}{2}

Solve for y

y=\frac{4x\cos(x)}{5\cos(x)-\sin(x)}

\nexists n_{3}\in \mathrm{Z}\text{ : }x=\pi n_{3}+\arcsin(\frac{5\sqrt{26}}{26})\text{ and }\nexists n_{2}\in \mathrm{Z}\text{ : }x=\pi n_{2}+\arctan(5)\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }x=\frac{\pi \left(2n_{1}+1\right)}{2}

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Trigonometry

5 problems similar to:

y = \frac { 4 x } { 5 - \tan ( x ) }

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How do you differentiate \displaystyle{y}=\frac{{x}}{{{2}-{\tan{{x}}}}} ?

https://socratic.org/questions/how-do-you-differentiate-y-x-2-tanx

\displaystyle\frac{{{2}-{\tan{{x}}}+{x}{{\sec}^{{2}}{x}}}}{{\left({2}-{\tan{{x}}}\right)}^{{2}}} Explanation: \displaystyle{y}=\frac{{x}}{{{2}-{\tan{{x}}}}} \displaystyle{\left(\frac{{d}}{{{\left.{d}{x}\right.}}}{\left(\frac{{u}}{{v}}\right)}=\frac{{{v}\frac{{{d}{u}}}{{{\left.{d}{x}\right.}}}-{u}\frac{{{d}{v}}}{{{\left.{d}{x}\right.}}}}}{{v}^{{2}}}\right)} ...

How do you graph, identify the domain, range, and asymptotes for \displaystyle{y}={\tan{{\left({2}{x}+\frac{\pi}{{2}}\right)}}} ?

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Domain: \displaystyle{x}\ne\frac{{k}}{{2}}\pi,{k}={0},\pm{1},\pm{2},\pm{3},.. Range: \displaystyle{\left(-\infty,\infty\right)} . Asymptotes: \displaystyle{x}=\frac{{k}}{{2}}\pi,{k}={0},\pm{1},\pm{2},\pm{3},.. ...

What is the implicit derivative of \displaystyle{1}=\frac{{x}}{{y}}-{x}{\tan{{y}}} ?

https://socratic.org/questions/what-is-the-implicit-derivative-of-1-x-y-xtany

\displaystyle\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}=-\frac{{{y}{\left({y}{\tan{{y}}}-{1}\right)}}}{{{x}{\left({1}+{y}^{{2}}{{\sec}^{{2}}{y}}\right)}}} Explanation: \displaystyle\frac{{d}}{{\left.{d}{x}\right.}}{\left[{1}=\frac{{x}}{{y}}-{x}{\tan{{y}}}\right]} ...

How do you find the period of \displaystyle{y}={\tan{{\left({x}-\frac{\pi}{{4}}\right)}}} ?

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The period is \displaystyle\pi Explanation: For a function with formula such as \displaystyle{y}={\tan{{\left({B}\cdot{x}-{C}\right)}}} the period is \displaystyle{T}=\frac{\pi}{{B}} and ...

How do you graph \displaystyle{y}={\tan{{\left({x}+{\left(\frac{\pi}{{2}}\right)}\right)}}} ?

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Look below. Explanation: graph{tan(x+(pi/2)) [-10, 10, -5, 5]}

How do you implicitly differentiate \displaystyle-{1}={x}{y}{\tan{{\left(\frac{{x}}{{y}}\right)}}} ?

https://socratic.org/questions/how-do-you-implicitly-differentiate-1-xytan-x-y

\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={\frac{{{y}}}{{{x}}}}\cdot{\frac{{{2}{x}{\csc{{\left({\frac{{{2}{x}}}{{{y}}}}\right)}}}+{y}}}{{{x}{\cot{{\left(\frac{{x}}{{y}}\right)}}}-{y}}}} ...

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