Question

question 17 (1 point)
for the angle \\( \theta = 210 ^ { \circ } \\) moving counter - clockwise in standard position, determine which primary trigonometric ratio is positive.
\\( \bigcirc \\) a) cosine
\\( \bigcirc \\) b) tangent
\\( \bigcirc \\) c) sine
\\( \bigcirc \\) d) none are positive

Explanation:

Step1: Determine the quadrant of the angle

An angle of \(210^{\circ}\) lies in the third quadrant (\(180^{\circ}<\theta = 210^{\circ}<270^{\circ}\)).

Step2: Recall the sign of trigonometric ratios in each quadrant

In the third quadrant, \(\sin\theta=\frac{y}{r}<0\) (since \(y < 0\) and \(r>0\)), \(\cos\theta=\frac{x}{r}<0\) (since \(x < 0\) and \(r>0\)), and \(\tan\theta=\frac{y}{x}>0\) (since \(x<0\) and \(y < 0\), so the ratio of two negative numbers is positive).

Answer:

B. tangent