Question

18 multiple choice 1 point
determine the sign (positive or negative) of the given value without use of
a calculator.
tan 259°
negative
positive
19 multiple choice 1 point
determine the sign (positive or negative) of the given value without use of
a calculator.
cos \\( \frac { \pi } { 5 } \\)
positive
negative

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:

1. B. Positive
2. A. Positive