Given theta = (3)/(5).

Step 1: Find the value of $\sin \theta$. Given $\cos \theta = \frac{3}{5}$. Using the Pythagorean identity $\sin^2 \theta + \cos^2 \theta = 1$: $$ \sin^2 \theta + \left(\frac{3}{5}\right)^2 = 1 $$ $$ \sin^2 \theta + \frac{9}{25} = 1 $$ $$ \sin^2 \theta = 1 - \frac{9}{25} $$ $$ \sin^2 \theta = \frac{25}{25} - \frac{9}{25} $$ $$ \sin^2 \theta = \frac{16}{25} $$ Taking the square root, we get: $$ \sin \theta = \pm \sqrt{\frac{16}{25}} = \pm \frac{4}{5} $$ Assuming $\theta$ is an acute angle (in the first quadrant), $\sin \theta$ is positive. $$ \sin \theta = \frac{4}{5} $$ Step 2: Simplify $\tan(90^\circ - \theta)$. Using the complementary angle identity, $\tan(90^\circ - \theta) = \cot \theta$. Step 3: Find the value of $\cot \theta$. We know that $\cot \theta = \frac{\cos \theta}{\sin \theta}$. Substitute the values of $\cos \theta$ and $\sin \theta$: $$ \cot \theta = \frac{\frac{3}{5}}{\frac{4}{5}} = \frac{3}{4} $$ Step 4: Substitute the values into the expression $\sin \theta - \tan(90^\circ - \theta)$. The expression becomes: $$ \sin \theta - \cot \theta $$ Substitute the values found in Step 1 and Step 3: $$ \frac{4}{5} - \frac{3}{4} $$ Step 5: Calculate the final value. To subtract the fractions, find a common denominator, which is $20$: $$ \frac{4 \times 4}{5 \times 4} - \frac{3 \times 5}{4 \times 5} $$ $$ \frac{16}{20} - \frac{15}{20} $$ $$ \frac{16 - 15}{20} $$ $$ \frac{1}{20} $$ The final answer is: $$ \boxed{\frac{1}{20}} $$ That's 2 down. 3 left today — send the next one.