Question

trig quiz
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question 33 (1 point)
for the angle \\( \theta=210^{\circ} \\) moving counter - clockwise in standard position, determine which primary trigonometric ratio is positive.
\\( \bigcirc \\) a) tangent
\\( \bigcirc \\) b) none are positive
\\( \bigcirc \\) c) sine
\\( \bigcirc \\) d) cosine
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Explanation:

Step1: Determine the quadrant of the angle

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

Step2: Recall the sign of trigonometric ratios in each quadrant

In the third quadrant, sine (\(\sin\theta=\frac{y}{r}\), \(y < 0\), \(r>0\)) and cosine (\(\cos\theta=\frac{x}{r}\), \(x < 0\), \(r>0\)) are negative. For tangent \(\tan\theta=\frac{\sin\theta}{\cos\theta}=\frac{y}{x}\), since \(x<0\) and \(y < 0\), \(\tan\theta=\frac{\text{negative}}{\text{negative}}=\text{positive}\).

Answer:

A. tangent