given sin theta = - 3/5 and csc theta - 5/3 in quadrant 3, find the value of other trigonometric functions using a Pythagorean Identity. Show your work.

cos theta = - 4/5.

sec theta = - 5/4.

tan theta = 3/4.

cot theta = 4/3.

Step-by-step explanation:

sin^2 theta + cos^2 theta = 1

(-3/5) ^2 + cos^2 theta = 1

cos^2 theta = 1 - 9/25

cos^2 theta = 16/25

cos theta = - 4/5 (negative because it is in Quadrant 3).

sec theta = 1 / cos theta = - 5/4.

tan theta = sin theta / cos theta = - 3/5 / - 4/5

= - 3/5 * - 5/4

= 3/4.

cot theta = 1 / tan theta = 4/3.