Solve the equation, e^x=4sinx ; x is greater than 0, less than 2pi.
how do i figure this out, and i have my ti-83 with me.
Hello,
If you use your TI-83, you could simply punch in the function:
$\displaystyle f(x)=e^{x}$
$\displaystyle g(x)=4\sin(x)$
The x you are searching for is the x-value at the intersection between the graphs of $\displaystyle f$ and $\displaystyle g$.
Can you input 'Ans' in your calculator (portable)? That means it can memorize the value obtained before and use the value in other calculation.
Set it to be about $\displaystyle 0.5 $
Then input
$\displaystyle \ln( 4\sin(Ans) ) $ and press ' Enter' followed by ' Enter' ,' Enter',' Enter',' Enter',.... until no observable change on the screen , then the value displayed on it is the solution . It is $\displaystyle 1.364958434...$
The key to find out the solution is to put one of the variable $\displaystyle x $ as the subject . Here we can put $\displaystyle x = \ln(4\sin(x))$ or $\displaystyle x = \sin^{-1}(\frac{e^x}{4})$
I also obtain the other solution , $\displaystyle 0.370558096...$