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To solve this problem, we are given:

- \(\frac{\pi}{2} < \theta < \pi\) (which indicates that \(\theta\) is in the second quadrant),
- \(\sin(\theta) = \frac{1}{4}\).

We need to evaluate:

1. \(\cos(\theta)\)
2. \(\tan(\theta)\)

### Step 1: Find \(\cos(\theta)\)

Since we know \(\sin(\theta) = \frac{1}{4}\), we can use the Pythagorean identity

Suppose \( \frac{\pi}{2} < \theta < \pi \), and \( \sin(\theta) = \frac{1}{4} \). Evaluate \( \cos(\theta) \) and \( \tan(\theta) \).

Learn how to find \( \cos(\theta) \) and \( \tan(\theta) \) when \( \sin(\theta) = \frac{1}{4} \) and \( \frac{\pi}{2} < \theta < \pi \) using trigonometric identities. This problem explores the Pythagorean identity and is suitable for students in Grades 10-12.

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