Question

use patterns to find the values of sin 30° and cos 30° and then compare their values. (1 point)
○ sin 30° < cos 30°
○ sin 30° > cos 30°
○ sin 30° = cos 30°
○ sin 30° = − cos 30°

Explanation:

Step1: Recall trigonometric values

We know the standard trigonometric values for special angles. For \(30^{\circ}\), \(\sin30^{\circ}=\frac{1}{2}\) and \(\cos30^{\circ}=\frac{\sqrt{3}}{2}\).

Step2: Compare the values

Now we compare \(\frac{1}{2}\) and \(\frac{\sqrt{3}}{2}\). Since \(\sqrt{3}\approx1.732\), so \(\frac{1}{2}=0.5\) and \(\frac{\sqrt{3}}{2}\approx0.866\). Clearly, \(0.5 < 0.866\), which means \(\sin30^{\circ}<\cos30^{\circ}\).

Answer:

A. \(\sin 30^{\circ} < \cos 30^{\circ}\)