Question

If 2sin theta = √3, (0° < theta <90° ), then find the value of theta

Answer 1

`2sin(\theta )+√(3)=0\implies 2sin(\theta )=-√(3)\implies sin(\theta )=-\cfrac{√(3)}{2} \\\\\\ sin^(-1)\left[ sin(\theta ) \right]=sin^(-1)\left( -\cfrac{√(3)}{2} \right) \implies \theta =sin^(-1)\left( -\cfrac{√(3)}{2} \right)\implies \theta \begin{cases} \stackrel{III~Quadrant}{(4\pi )/(3)}\\\\ \stackrel{IV~Quadrant}{(5\pi )/(3)} \end{cases}`

check your Unit Circle.