Question

question 31 (1 point) for the angle θ = 210° moving counter - clockwise in standard position, determine which primary trigonometric ratio is positive. a) none are positive b) tangent c) cosine d) sine

Explanation:

Step1: Determine the quadrant of the angle

The angle \(\theta = 210^{\circ}\). Since \(180^{\circ}<210^{\circ}<270^{\circ}\), the angle \(210^{\circ}\) is in the third quadrant.

Step2: Recall the sign of trigonometric functions in each quadrant

In the third quadrant, \(\sin\theta=\frac{y}{r}<0\) (because \(y < 0\) and \(r>0\)), \(\cos\theta=\frac{x}{r}<0\) (because \(x < 0\) and \(r>0\)), and \(\tan\theta=\frac{y}{x}>0\) (because \(x<0\) and \(y < 0\), so the quotient is positive).

Answer:

C. tangent