B

Given: The T-ratio is defined as tan(θ) = -3/4 in the second quadrant where θ lies.

Step 1: Determine sin(θ) and cos(θ) using the identity for tangent:
$$ tan(θ) = \frac{sin(θ)}{cos(θ)} $$
Given that tan(θ) = -3/4, we can assume:
$$ sin(θ) = -3k \text{ and } cos(θ) = 4k $$
Step 2: Since θ is in the second quadrant:
- sin(θ) is positive and cos(θ) is negative.
Therefore, $$ sin(θ) = 3k \text{ and } cos(θ) = -4k $$
Step 3: Use the Pythagorean identity:
$$ sin^2(θ) + cos^2(θ) = 1 $$
Substituting:
$$ (3k)^2 + (-4k)^2 = 1 $$
$$ 9k^2 + 16k^2 = 1 $$
$$ 25k^2 = 1 $$
$$ k^2 = \frac{1}{25} $$
$$ k = \frac{1}{5} $$
Step 4: Now we can find sin(θ) and cos(θ):
$$ sin(θ) = 3 \cdot \frac{1}{5} = \frac{3}{5} $$
$$ cos(θ) = -4 \cdot \frac{1}{5} = -\frac{4}{5} $$
Step 5: Find other T-ratios:

• $$ tan(θ) = \frac{sin(θ)}{cos(θ)} = \frac{3/5}{-4/5} = -\frac{3}{4} $$
• $$ sec(θ) = \frac{1}{cos(θ)} = -\frac{5}{4} $$
• $$ csc(θ) = \frac{1}{sin(θ)} = \frac{5}{3} $$
• $$ cot(θ) = \frac{1}{tan(θ)} = -\frac{4}{3} $$
• $$ cos(θ) = -\frac{4}{5} $$

Conclusion: The values of the other five T-ratios are:
$$ sec(θ) = -\frac{5}{4}, csc(θ) = \frac{5}{3}, cot(θ) = -\frac{4}{3}. $$