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what angle has a tangent and sine that are both negative?

300
210
45
150

$$300^{\circ}$$
$$\text{In quadrant IV, both ratios of tangent and sine are negative.}\\ \\300^{\circ}~ \text{lies in the fourth quadrant, so}~ \tan 300^{\circ} ~ \text{and}~ \sin 300^{\circ}~ \text{are negative.}$$