Question

question 31 (1 point)page 31 of 35for the angle ( \theta = 210^{circ} ) moving counter - clockwise in standard position, determine whichprimary trigonometric ratio is positive.a) none are positiveb) sinec) cosined) tangent

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 (\(\sin\theta=\frac{y}{r}\)): \(y < 0\), \(r>0\), so \(\sin\theta<0\).
• Cosine (\(\cos\theta=\frac{x}{r}\)): \(x < 0\), \(r>0\), so \(\cos\theta<0\).
• Tangent (\(\tan\theta=\frac{y}{x}\)): \(x < 0\), \(y < 0\), so \(\tan\theta=\frac{\text{negative}}{\text{negative}}> 0\).

Answer:

D. tangent