Math CentralQuandaries & Queries


Question from Ruth, a student:

I'm trying to find two values of x satisfying f(x)=1 where f(x)=sin(ln(x))

Hi Ruth,

I am not sure if you are measuring angles using degrees or radians. In any case you need to find the angle measure $y$ so that $\sin(y) = 1.$ Once you have this numeric value $y$ you can use the exponential function to solve $y = \ln(x)$ for $x.$

You are asked for two values of $x$ so you need another angle measure $y$ so that $\sin(y) = 1$ and then for this value of $y$ solve $y = \ln(x)$ for $x.$ There are many values of $y$ so that $\sin(y) = 1$ but if $y$ is negative then $y = \ln(x)$ has no solution so you need a positive value for $y.$


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