Evaluating Trigonometric Ratios for 60 Degrees

The question asks for the value of the expression \(\frac{\sin 60^\circ}{\cos 60^\circ}\).

Using Trigonometric Identity

Recall the fundamental trigonometric identity:

\(\tan \theta = \frac{\sin \theta}{\cos \theta}\)

Applying this identity to the given expression with \(\theta = 60^\circ\):

\(\frac{\sin 60^\circ}{\cos 60^\circ} = \tan 60^\circ\)

Calculating the Value

We know the standard trigonometric values for \(60^\circ\):

• \(\sin 60^\circ = \frac{\sqrt{3}}{2}\)
• \(\cos 60^\circ = \frac{1}{2}\)

Substitute these values into the expression:

\(\frac{\sin 60^\circ}{\cos 60^\circ} = \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\)

To simplify the division of fractions, multiply the numerator by the reciprocal of the denominator:

\(\frac{\sqrt{3}}{2} \times \frac{2}{1} = \sqrt{3}\)

Alternatively, knowing that \(\tan 60^\circ = \sqrt{3}\) directly gives the answer.

Final Answer Determination

The calculated value is \(\sqrt{3}\). This corresponds to Option A.