What is the tangent of arcsin(x/7) ?

The tangent of arcsin(x/7) is y= 1/(sqrt(49-a_{0)^2)}x+arcsin((a_{0})/7)-(a_{0})/(sqrt(49-a_{0)^2)}

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tangent of arcsin(x/7)

tangent of

arcsin (\frac{x}{7})

y = \frac{1}{49 - a _{0}^{2}} x + arcsin (\frac{a _{0}}{7}) - \frac{a _{0}}{49 - a _{0}^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, arcsin (\frac{a _{0}}{7}))

Find the slope of

y = arcsin (\frac{x}{7}) : \frac{d y}{d x} = \frac{1}{49 - x ^{2}}

Compute the slope of

y = arcsin (\frac{x}{7})

x = a_{0} : m = \frac{1}{49 - a _{0}^{2}}

Find the line with slope m=

\frac{1}{49 - a _{0}^{2}}

and passing through

(a_{0}, arcsin (\frac{a _{0}}{7})) : y = \frac{1}{49 - a _{0}^{2}} x + arcsin (\frac{a _{0}}{7}) - \frac{a _{0}}{49 - a _{0}^{2}}

y = \frac{1}{49 - a _{0}^{2}} x + arcsin (\frac{a _{0}}{7}) - \frac{a _{0}}{49 - a _{0}^{2}}

y^{^{'}} = \frac{x ^{2} + 2 \cdot y ^{2}}{x \cdot y}

\frac{d}{d x} (10 x sin (x))

9 x^{2} y^{2} + x^{\frac{3}{2}} y^{^{'}} = y^{2}

(x^{2} - 18) (2 x + 3)

\int x + \frac{1}{x ^{2}} d x

What is the tangent of arcsin(x/7) ?
The tangent of arcsin(x/7) is y= 1/(sqrt(49-a_{0)^2)}x+arcsin((a_{0})/7)-(a_{0})/(sqrt(49-a_{0)^2)}