QPaperGen

Given:\(
\sin x = \frac{3}{5}, \quad x \text{ lies in the second quadrant}
\)\[\]

Since \(\sin x = \frac{3}{5}\):

\[
\sin^2 x + \cos^2 x = 1
\]
\[
\left(\frac{3}{5}\right)^2 + \cos^2 x = 1
\]
\[
\frac{9}{25} + \cos^2 x = 1
\]
\[
\cos^2 x = 1 - \frac{9}{25} = \frac{16}{25}
\]
\[
\cos x = -\frac{4}{5}
\]
(Negative in the second quadrant)

\[
\tan x = \frac{\sin x}{\cos x} = \frac{3/5}{-4/5} = -\frac{3}{4}
\]

\[
\cot x = \frac{\cos x}{\sin x} = \frac{-4/5}{3/5} = -\frac{4}{3}
\]

\[
\sec x = \frac{1}{\cos x} = -\frac{5}{4}
\]

\[
\csc x = \frac{1}{\sin x} = \frac{5}{3}
\]

Summary Table:

\[
\begin{array}{|c|c|}
\hline
\text{Function} & \text{Value} \\
\hline
\sin x & \dfrac{3}{5} \\
\cos x & -\dfrac{4}{5} \\
\tan x & -\dfrac{3}{4} \\
\cot x & -\dfrac{4}{3} \\
\sec x & -\dfrac{5}{4} \\
\csc x & \dfrac{5}{3} \\
\hline
\end{array}
\]