Answer:1) secФ = √2 ⇒ 2nd answer2) The best identity is 1 + cot²Ф = csc²Ф ⇒ 4th answer3) The expression 1/(-3/8) is equivalent to cotФ ⇒ 1st answerStep-by-step explanation:* The angle Ф lies in the 4th quadrant because 2π/3 < Ф < 2π∴ The values of cosФ and secФ only positive* Use the identity sec²Ф = tan²Ф + 1∵ tanФ = -1∴ sec²Ф = (-1)² + 1 = 1 + 1 = 2 ⇒ take √ in both sides∴ secФ = ± √2∵ Ф lies in the 4th quadrant∴ secФ = √2 * Remember if we have the value of cotФ, we can use the identity cot²Ф + 1 = csc²Ф to find the value of cscФ∵ cscФ = 1/sinФ∴ sinФ = 1/cosФ* In the problem Fatma know that cotФ = 4/7∵ She wants to know the value of sinФ∴ She can use the identity cot²Ф + 1 = csc²Ф* The best identity is cot²Ф + 1 = csc²Ф * We know that cotФ = 1/tanФ∵ tanФ = -3/8∴ cotФ = 1/(-3/8)∴ The expression 1/(-3/8) is equivalent to cotФ