# Thread: solve 2sin(x-45)=1

1. ## solve 2sin(x-45)=1

Solve the equation $\displaystyle 2sin(x-45^0) = 1$ for $\displaystyle 0^0<x<360^0$

2. Just work your way backwards:

$\displaystyle 2\sin(x-45^{\circ}) = 1$

$\displaystyle \sin(x-45^{\circ}) = \frac{1}{2}$

$\displaystyle x-45^{\circ} = \sin^{-1}\left(\frac{1}{2}\right)$

Can you carry on?

3. Solve it the way you normally would

$\displaystyle 2\sin{(x - 45^{\circ})} = 1$

$\displaystyle \sin{(x - 45^{\circ})} = \frac{1}{2}$

$\displaystyle x - 45^{\circ} = \left\{30^{\circ}, 180^{\circ} - 30^{\circ}\right\}$

$\displaystyle x - 45^{\circ} = \left\{30^{\circ}, 150^{\circ}\right\}$

$\displaystyle x = \left\{30^{\circ} + 45^{\circ}, 150^{\circ} + 45^{\circ}\right\}$

$\displaystyle x = \left\{75^{\circ}, 195^{\circ}\right\}$.