1. The problem asks to find $\sin 30^\circ$, $\cos 30^\circ$, and $\tan 30^\circ$. 2. Recall the definitions and values of sine, cosine, and tangent for special angles. For $30^\circ$, these are well-known from the unit circle and special triangles. 3. Using the 30-60-90 right triangle or unit circle: - $\sin 30^\circ = \frac{1}{2}$ - $\cos 30^\circ = \frac{\sqrt{3}}{2}$ - $\tan 30^\circ = \frac{\sin 30^\circ}{\cos 30^\circ} = \frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}} = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}$ 4. Explanation: The sine of an angle in a right triangle is the ratio of the length of the side opposite the angle to the hypotenuse. For $30^\circ$, this ratio is $\frac{1}{2}$. 5. The cosine is the ratio of the adjacent side to the hypotenuse, which is $\frac{\sqrt{3}}{2}$ for $30^\circ$. 6. The tangent is the ratio of sine to cosine, simplifying to $\frac{\sqrt{3}}{3}$. Final answers: $$\sin 30^\circ = \frac{1}{2}, \quad \cos 30^\circ = \frac{\sqrt{3}}{2}, \quad \tan 30^\circ = \frac{\sqrt{3}}{3}$$