Equations in Radians

On [0, 2π) nothing changes but the units: π takes the place of 180°. Solve $2\sin\left(x\right)-\sqrt{2} = 0$: $\sin\left(x\right) = \frac{\sqrt{2}}{2}$, the reference angle is π/4, and the quadrant II partner is $\pi-\frac{\pi}{4}$. Write π as 4π/4: four quarters minus one is three quarters, so x = π/4 or 3π/4.

The partners in radians: quadrant II is π − r, quadrant III is π + r, quadrant IV is 2π − r.