Question

\(\tan 30^\circ = \)

• A. \(\sqrt{3}\)
• B. \(\frac{\sqrt{3}}{2}\)
• C. \(\frac{1}{\sqrt{3}}\)
• D. 1

Hint:

Memorizing the trigonometric values for 0°, 30°, 45°, 60°, and 90° is essential for speed and accuracy in exams. For tangent, remember the pattern: 0, \(1/\sqrt{3}\), 1, \(\sqrt{3}\), undefined.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This question asks for the standard value of the tangent function for the angle 30 degrees.

Step 2: Key Formula or Approach:
The value of \(\tan 30^\circ\) is a fundamental trigonometric ratio that should be memorized. It can also be derived from the ratio \(\frac{\sin 30^\circ}{\cos 30^\circ}\).
We know \(\sin 30^\circ = \frac{1}{2}\) and \(\cos 30^\circ = \frac{\sqrt{3}}{2}\).

Step 3: Detailed Explanation:
Using the ratio definition:
\[ \tan 30^\circ = \frac{\sin 30^\circ}{\cos 30^\circ} = \frac{1/2}{\sqrt{3}/2} \] \[ = \frac{1}{2} \times \frac{2}{\sqrt{3}} \] \[ = \frac{1}{\sqrt{3}} \] This is a standard value.

Step 4: Final Answer:
The value of \(\tan 30^\circ\) is \(\frac{1}{\sqrt{3}}\).