How do you find at equation of the tangent line to the graph \displaystyle{y}=\frac{{{\cos{{x}}}}}{{{\sin{{x}}}+{2}}} at x =pi/2?
https://socratic.org/questions/how-do-you-find-at-equation-of-the-tangent-line-to-the-graph-y-cosx-sinx-2-at-x-
\displaystyle{y}=\frac{\pi}{{6}}-\frac{{1}}{{3}}{x} Explanation:Start by finding the y-coordinate of tangency.\displaystyle{y}=\frac{{\cos{{\left(\frac{\pi}{{2}}\right)}}}}{{{\sin{{\left(\frac{\pi}{{2}}\right)}}}+{2}}} ...

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How do you determine graphically and analytically whether \displaystyle{y}_{{1}}=\frac{{\cos{{x}}}}{{\sin{{x}}}} is equivalent to \displaystyle{y}_{{2}}={\cot{{x}}} ?
https://socratic.org/questions/how-do-you-determine-graphically-and-analytically-whether-y-1-cosx-sinx-is-equiv
Dean R. Apr 23, 2018 Since\displaystyle{\cot{{x}}}={\frac{{{\cos{{x}}}}}{{{\sin{{x}}}}}}by definition, there's no reason or meaning to graphically or analytically verifying this, so I ...
How do you use the quotient rule to find the derivative of \displaystyle{y}=\frac{{{1}+{\cos{{\left({x}\right)}}}}}{{{1}+{\sin{{\left({x}\right)}}}}} ?
https://socratic.org/questions/how-do-you-use-the-quotient-rule-to-find-the-derivative-of-y-1-cos-x-1-sin-x
Psykolord1989 . · Amory W. Sep 9, 2014 The quotient rule states that given functions u and v such that\displaystyle{y}=\frac{{{u}{\left({x}\right)}}}{{{v}{\left({x}\right)}}},\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}=\frac{{{u}'{\left({x}\right)}{v}{\left({x}\right)}-{u}{\left({x}\right)}{v}'{\left({x}\right)}}}{{{v}^{{2}}{\left({x}\right)}}} ...
How do you find the exact value \displaystyle{\tan{{\left({x}-{y}\right)}}} if \displaystyle{\sin{{x}}}=\frac{{8}}{{17}},{\cos{{y}}}=\frac{{3}}{{5}} ?
The answer is\displaystyle=-\frac{{36}}{{77}} Explanation:We use \displaystyle{{\cos}^{{2}}{x}}+{{\sin}^{{2}}{x}}={1}\displaystyle{{\cos}^{{2}}{y}}+{{\sin}^{{2}}{y}}={1}\displaystyle{\sin{{\left({x}-{y}\right)}}}={\sin{{x}}}{\cos{{y}}}-{\sin{{y}}}{\cos{{x}}} ...

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How do you differentiate \displaystyle{y}={3}{x}{\cos{{\left(\frac{{x}}{{3}}\right)}}}-{\sin{{\left(\frac{{x}}{{3}}\right)}}} ?
the answer \displaystyle{y}'=\frac{{{8}{\cos{{\left(\frac{{x}}{{3}}\right)}}}}}{{3}}-{x}{\sin{{\left(\frac{{x}}{{3}}\right)}}} Explanation:show below \displaystyle{y}={3}{x}{\cos{{\left(\frac{{x}}{{3}}\right)}}}-{\sin{{\left(\frac{{x}}{{3}}\right)}}} ...
How do you simplify \displaystyle\frac{{\cos{{\left({x}-{y}\right)}}}}{{\sin{{\left({x}-{y}\right)}}}} to trigonometric functions of x and y?
https://socratic.org/questions/how-do-you-simplify-cos-x-y-sin-x-y-to-trigonometric-functions-of-x-and-y-1
Simplify trig expressionExplanation: \displaystyle\frac{{{\cos{{\left({x}-{y}\right)}}}}}{{{\sin{{\left({x}-{y}\right)}}}}} =\displaystyle=\frac{{{\cos{{x}}}.{\cos{{y}}}+{\sin{{x}}}.{\sin{{y}}}}}{{{\sin{{x}}}.{\cos{{y}}}-{\sin{{y}}}.{\cos{{x}}}}}
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