https://r2.erweima.ai/mathbot/image/1726581791108zwh1ovqk.jpg

The image shows the trigonometric equation:

\[
\cos \theta = \frac{\sqrt{3}}{2}
\]
with the condition that \(\theta\) belongs to the first quadrant (\(\theta \in\) primer cuadrante).

### Solution:
We know from standard trigonometric values that:

\[
\cos \left( \frac{\pi}{6} \right) = \frac{\sqrt{3}}{2}
\]

Thus, \(\theta = \frac{\pi}{6}\) or \(30^\circ\) is the solution. Since the problem specifies that \(\theta\) is in the first quadrant, there are no additional solutions.

### Final answer:
\[
\theta = \frac{\pi}{6} \text{ or } 30^\circ
\]

Would you like further details or have any other questions?

Here are 5 related questions:
1. What is the value of \(\sin(\theta)\) when \(\theta = 30^\circ\)?
2. How do trigonometric values change in different quadrants?
3. What is the general solution for \(\cos \theta = \frac{\sqrt{3}}{2}\)?
4. Can you find the tangent of \(\theta\) for \(\theta = 30^\circ\)?
5. What other angles in degrees correspond to the cosine value of \(\frac{\sqrt{3}}{2}\) in the unit circle?

**Tip:** In the first quadrant, all trigonometric functions (sine, cosine, and tangent) are positive.

cos(θ) = √3/2, with θ in the first quadrant

Learn how to solve the trigonometric equation cos(θ) = √3/2 with θ in the first quadrant. Discover key concepts in trigonometry, such as the standard values of cosine and unit circle properties. Suitable for high school students in Grades 10-12.

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