Final answer:
The cotangent of ∅ in quadrant III is 1/2.
Step-by-step explanation:
The question asks to find the value of cot ∅ given that ∅ = -2 and it is in quadrant III.
The value of ∅ in quadrant III can be determined by adding 180 degrees to the reference angle in quadrant I, which is 2 degrees. Therefore, ∅ in quadrant III is 180 + 2 = 182 degrees.
The cotangent of an angle ∅ is equal to the ratio of the adjacent side to the opposite side of a right triangle formed by the angle. In quadrant III, both the adjacent and opposite sides are negative. So, we can use the values from the given components Cx = −2/3, Cy = −4/3, and C₂ = 7/3 to calculate the cotangent of 182 degrees using the equation cot ∅ = -Cx / Cy. Therefore, cot ∅ = -(-2/3) / (-4/3) = 2/4 = 1/2.