Question

Urgent!! will mark brainliest!

Answer 1

Answer:

1) secФ = √2 ⇒ 2nd answer

2) The best identity is 1 + cot²Ф = csc²Ф ⇒ 4th answer

3) The expression 1/(-3/8) is equivalent to cotФ ⇒ 1st answer

Step-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