Final answer:
To find tax and six given secx=(6)/(5) with sinx>0, we derive cost from sex, use the Pythagorean identity to calculate six, and then compute tax using the ratio of six to cosx, resulting in sinx=\(\frac{\sqrt{11}}{6}\) and tanx=\(\frac{\sqrt{11}}{5}\).
Step-by-step explanation:
Given that sex = \( \frac{6}{5} \) and six is positive, we can find tax and six.
Firstly, recall that secx = \( \frac{1}{\cos x} \). Since secx = \( \frac{6}{5} \), we have cosx = \( \frac{5}{6} \).
To find six, we use the Pythagorean identity: sin^2x + cos^2x = 1, which gives six = \sqrt{1 - cos^2x}. Substituting cosx in, we get sinx = \sqrt{1 - \( \frac{5}{6} \)^2} = \sqrt{1 - \( \frac{25}{36} \)} = \sqrt{\( \frac{11}{36} \)} = \( \frac{\sqrt{11}}{6} \).
Since tanx = \( \frac{sinx}{cosx} \), we can compute tanx = \( \frac{\sqrt{11}}{6} \) divided by \( \frac{5}{6} \), resulting in tanx = \( \frac{\sqrt{11}}{5} \).