Question

If \( \sin\theta = \dfrac{3}{4} \), then the value of \( \tan\theta \) will be:

• A. $\dfrac{3}{\sqrt{7}}$
• B. $\dfrac{4}{\sqrt{7}}$
• C. $\dfrac{3}{5}$
• D. $\dfrac{4}{5}$

Hint:

When \( \sin\theta \) is given, use \( \cos\theta = \sqrt{1 - \sin^2\theta} \) and \( \tan\theta = \frac{\sin\theta}{\cos\theta} \).

Answer 1

The Correct Option is A

Step 1: Recall the identity.
\[ \sin^2\theta + \cos^2\theta = 1 \]
Step 2: Find \( \cos\theta \).
\[ \cos\theta = \sqrt{1 - \sin^2\theta} = \sqrt{1 - \left(\frac{3}{4}\right)^2} = \sqrt{1 - \frac{9}{16}} = \sqrt{\frac{7}{16}} = \frac{\sqrt{7}}{4} \]
Step 3: Find \( \tan\theta \).
\[ \tan\theta = \frac{\sin\theta}{\cos\theta} = \frac{\frac{3}{4}}{\frac{\sqrt{7}}{4}} = \frac{3}{\sqrt{7}} \]
Step 4: Conclusion.
Hence, the value of \( \tan\theta \) is \( \boxed{\dfrac{3}{\sqrt{7}}} \).