Step 1a

To find csc⁡(α), we first need to determine the sine of α since \$"csc"⁡(α) = 1/("sin"⁡(α))\$.
Given that \$"cot"⁡(α) = 5/12\$​, and α is in Quadrant II, we can use the Pythagorean identity to find the sine of α.

In Quadrant II:

\$"cot"⁡(α) = "adjacent"/"opposite" = 5/12\$

Explanation: In Quadrant II, apply the Pythagorean theorem to determine sinα, with adjacent side 5 and opposite side 12.

Step 1b

Then use the Pythagorean theorem to find the hypotenuse:

\$c^2 = a^2 + b^2\$

\$c^2 = 5^2 + 12^2\$

\$c = \sqrt(169)\$

c = 13

So, the hypotenuse c = 13.

Explanation: Utilize Pythagorean theorem for determining the length of the hypotenuse.

Step 1c

Next, find the sine of α using the triangle:

\$sin(α) = "opposite"/"hypotenuse" = 12/13\$

Finally, to find csc⁡(α): \$csc(α) = 1/(sin(α))\$

​= \$1 /(12/13)\$

\$= 13/12\$

So, \$csc⁡(α) = 13/12\$.​

Explanation: Substitute hypotenuse in sin(α), simplify, then plug sin(α) in csc(α) formula to find csc(α).