https://file.aiquickdraw.com/mathbot/file/17257192793779p99vh2f.jpg

The equation provided in the image is:

\[
\sin \theta = \frac{3}{4}
\]
And the question is asking to find the value of \(\cos \theta\), given that \(\theta\) is an acute angle.

We can solve this using the Pythagorean identity:

\[
\sin^2 \theta + \cos^2 \theta = 1
\]

Now, let's substitute \(\sin \theta = \frac{3}{4}\) into the identity:

\[
\left(\frac{3}{4}\right)^2 + \cos^2 \theta = 1
\]

Solving for \(\cos \theta\):

\[
\frac{9}{16} + \cos^2 \theta = 1
\]
\[
\cos^2 \theta = 1 - \frac{9}{16} = \frac{16}{16} - \frac{9}{16} = \frac{7}{16}
\]
\[
\cos \theta = \sqrt{\frac{7}{16}} = \frac{\sqrt{7}}{4}
\]

So, \(\cos \theta = \frac{\sqrt{7}}{4}\).

### In Bengali:
\[
\sin \theta = \frac{3}{4}
\]
এবং প্রশ্নটি বলছে \(\cos \theta\) নির্ণয় করতে, যেখানে \(\theta\) একটি তীক্ষ্ণ কোণ। আমরা পাইথাগোরাস সূত্র ব্যবহার করতে পারি:

\[
\sin^2 \theta + \cos^2 \theta = 1
\]

এখন, \(\sin \theta = \frac{3}{4}\) বসালে পাই:

\[
\left(\frac{3}{4}\right)^2 + \cos^2 \theta = 1
\]
\[
\frac{9}{16} + \cos^2 \theta = 1
\]
\[
\cos^2 \theta = 1 - \frac{9}{16} = \frac{16}{16} - \frac{9}{16} = \frac{7}{16}
\]
\[
\cos \theta = \sqrt{\frac{7}{16}} = \frac{\sqrt{7}}{4}
\]

অতএব, \(\cos \theta = \frac{\sqrt{7}}{4}\).

---

Do you want more details or have any questions? Here are some related questions you can explore:

1. How can you calculate \(\tan \theta\) using \(\sin \theta\) and \(\cos \theta\)?
2. What are the exact values of \(\sin\), \(\cos\), and \(\tan\) for standard angles like \(30^\circ\), \(45^\circ\), and \(60^\circ\)?
3. How can the Pythagorean identity be used to verify trigonometric values for any acute angle?
4. What is the general formula for finding \(\cos \theta\) when \(\sin \theta\) is given?
5. How do trigonometric functions apply to right triangles in real-world problems?

**Tip**: The Pythagorean identity is a fundamental tool in trigonometry for switching between sine and cosine values.

Given that sin(θ) = 3/4, find the value of cos(θ). Also, θ is an acute angle.

Learn how to solve for cos(θ) when sin(θ) = 3/4 using the Pythagorean identity in trigonometry. The solution covers step-by-step instructions and is suitable for students in grades 9-12.

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