18 multiple choice 1 point\ndetermine the sign (positive or negative) of the given value without use of\na…

Explanation:

Step1: Determine the quadrant of (259^{\circ})

Since (180^{\circ}<259^{\circ}<270^{\circ}), (259^{\circ}) is in the third quadrant. In the third quadrant, both (x) (cosine) and (y) (sine) are negative. Since (\tan\theta=\frac{\sin\theta}{\cos\theta}), and (\sin259^{\circ}<0), (\cos259^{\circ}<0), then (\tan259^{\circ}=\frac{\text{negative}}{\text{negative}}=\text{positive}).

Step2: Determine the quadrant of (\frac{\pi}{5})

Since (0 <\frac{\pi}{5}<\frac{\pi}{2}), (\frac{\pi}{5}) is in the first quadrant. In the first quadrant, (x) (cosine) is positive. So (\cos\frac{\pi}{5}>0).

Answer:

18. B. Positive
19. A. Positive