If `tantheta=sqrt(3)`,then find the value of `sintheta`.

Answer

To find the value of \( \sin \theta \) given that \( \tan \theta = \sqrt{3} \), we can follow these steps:

### Step 1: Understand the relationship between tangent and sine
We know that:
\[ \tan \theta = \frac{\sin \theta}{\cos \theta} \]
Given that \( \tan \theta = \sqrt{3} \), we can express this as:
\[ \frac{\sin \theta}{\cos \theta} = \sqrt{3} \]

### Step 2: Identify the angle
From trigonometric ratios, we know that:
\[ \tan 60^\circ = \sqrt{3} \]
Thus, we can conclude that:
\[ \theta = 60^\circ \]

### Step 3: Find the value of \( \sin \theta \)
Now that we have \( \theta = 60^\circ \), we can find \( \sin \theta \):
\[ \sin 60^\circ = \frac{\sqrt{3}}{2} \]

### Final Answer
Thus, the value of \( \sin \theta \) is:
\[ \sin \theta = \frac{\sqrt{3}}{2} \]

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