multiple choice 1 point give the exact value. sec 210° 2√3/3 -√2 -2√3/3 √2 2 multiple choice 1 point give…

Explanation:

Step1: Recall the definition of secant

$\sec\theta=\frac{1}{\cos\theta}$

Step2: Find the reference angle for (210^{\circ})

The reference angle for (210^{\circ}) is (210^{\circ}- 180^{\circ}=30^{\circ}). And (210^{\circ}) is in the third - quadrant, where (\cos\theta<0). So (\cos210^{\circ}=-\cos30^{\circ}=-\frac{\sqrt{3}}{2})

Step3: Calculate (\sec210^{\circ})

Since (\sec210^{\circ}=\frac{1}{\cos210^{\circ}}), substituting (\cos210^{\circ}=-\frac{\sqrt{3}}{2}), we get (\sec210^{\circ}=\frac{1}{-\frac{\sqrt{3}}{2}}=-\frac{2}{\sqrt{3}}=-\frac{2\sqrt{3}}{3})

Step4: Find the reference angle for (240^{\circ})

The reference angle for (240^{\circ}) is (240^{\circ}-180^{\circ} = 60^{\circ}). And (240^{\circ}) is in the third - quadrant, where (\cos\theta<0). So (\cos240^{\circ}=-\cos60^{\circ}=-\frac{1}{2})

Step5: Calculate (\sec240^{\circ})

Since (\sec240^{\circ}=\frac{1}{\cos240^{\circ}}), substituting (\cos240^{\circ}=-\frac{1}{2}), we get (\sec240^{\circ}=\frac{1}{-\frac{1}{2}}=- 2)

Answer:

1. (-\frac{2\sqrt{3}}{3})
2. (-2)