To find the value of \( \tan(8) \), we can use the relationship between the trigonometric functions. We know that:
- \( \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} \)
- \( \sec(\theta) = \frac{1}{\cos(\theta)} \)
From the given information, we have:
- \( \sec(8) = \frac{\sqrt{26}}{5} \)
- \( \sin(8) = 0 \)
First, we can find \( \cos(8) \):
\( \sec(8) = \frac{1}{\cos(8)} \)
\( \cos(8) = \frac{1}{\sec(8)} = \frac{5}{\sqrt{26}} \)
Next, since we know the value of \( \sin(8) \), let’s plug that into our tangent formula. Given that \( \sin(8) = 0 \):
\( \tan(8) = \frac{\sin(8)}{\cos(8)} = \frac{0}{\frac{5}{\sqrt{26}}} = 0 \)
Therefore, the value of \( \tan(8) \) is:
0
In summary, given the conditions that \( \sec(8) = \frac{\sqrt{26}}{5} \) and \( \sin(8) = 0 \), we conclude that:
Result: \( \tan(8) = 0 \)