Evaluate the a) \( \tan 240^{\circ} \) b) \( \sin 300^{\circ} \)

The angle \(240^{\circ}\) is in the third quadrant, where the tangent function is positive. To evaluate \( \tan 240^{\circ} \), we can use the reference angle, which is \(240^{\circ} - 180^{\circ} = 60^{\circ}\). The tangent of \(60^{\circ}\) is \(\sqrt{3}\), so: \[ \tan 240^{\circ} = \tan(60^{\circ}) = \sqrt{3} \] For the angle \(300^{\circ}\), it’s in the fourth quadrant, where the sine function is negative. The reference angle here is \(360^{\circ} - 300^{\circ} = 60^{\circ}\). The sine of \(60^{\circ}\) is \(\frac{\sqrt{3}}{2}\), hence: \[ \sin 300^{\circ} = -\sin(60^{\circ}) = -\frac{\sqrt{3}}{2} \]