Solve the equation 4 + 3 sin (2x – 1) = 6 for 0 < x < pi/2. please help me solve this equation
$\displaystyle \displaystyle 4 + 3\sin{(2x-1)} = 6$
$\displaystyle \displaystyle 3\sin{(2x-1)} = 2$
$\displaystyle \displaystyle \sin{(2x-1)} = \frac{2}{3}$
$\displaystyle \displaystyle 2x-1 = \arcsin{\left(\frac{2}{3}\right)}$
$\displaystyle \displaystyle 2x = 1 + \arcsin{\left(\frac{2}{3}\right)}$
$\displaystyle \displaystyle x = \frac{1}{2} + \frac{1}{2}\arcsin{\left(\frac{2}{3}\right)}$
Are you saying that you do not know what "radians" are? Do you understand what the condition you stated, "$\displaystyle 0\le x\le \pi/2$" means?
If you are using a calculator to find arcsin(2/3), do you know how to set the "mode" of your calculator? For example, the calculator that comes with Windows has buttons that give "Degrees", "Radians", and "Grad".