How do you find an equation of the tangent line to the curve $y = arcsin(x/2)$ at the point where $x = −sqrt2$ ?

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How do you find an equation of the tangent line to the curve $y = arcsin(x/2)$ at the point where $x = −sqrt2$ ?

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Answer 1 · 2015-04-13T15:22:58

First find the derivative of arcsin $(x/2)$ . It would be $1/2$ $1/sqrt(1-x^2/4)$ . This would give the slope of the tangent line at any given point of which x coordinate is known. In the present case it is x= - $sqrt2$ .

The slope would accordingly be $1/2$ $1/sqrt(1-2/4)$ = $1/sqrt2$ .

For x= - $sqrt2$ , y= arcsin $(-sqrt2 /2)$ = $-pi/4$ .

Equation of tangent line, in the point slope form, would be y+ $pi/4$ = $1/sqrt2$ ( x + $sqrt2)$

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How do you find an equation of the tangent line to the curve $y = arcsin(x/2)$ at the point where $x = −sqrt2$ ?

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How do you find an equation of the tangent line to the curve $y = arcsin(x/2)$ at the point where $x = −sqrt2$ ?