Question

Find sec x if sin x = -7/25 and cot x = -24/7. Show work.

Answer 1

Answer:

25/24

Step-by-step explanation:

sin x = O/H = -7/25

cot x = A/O = -24/7

sec x = H/A

if sin x = -7/25, the opposite side is 7, and the hypotenuse is 25

if cot x = -24/y, the adjacent side is 24 (and the opposite side is still 7)

since H = 25 and A = 24, sec x = 25/24

Also, you know it's positive because when sin x is negative, the angle is in quadrants 3 or 4, and when cot x is negative, the angle is in quandrants 2 or 4, so the only quadrant that satisfies both is 4. In quadrant 4, sec x is positive.

Answer 2

Answer:

25 / 24

Step-by-step explanation:

Given,

sin x = - 7 / 25

cot x = - 24 / 7

To find : sec x = ?

Identity : -

sin θ = opposite / hypotenuse

cot θ = adjacent / opposite

Similarly,

sin x = - 7 / 5

opposite / hypotenuse = - 7 / 5

Therefore,

opposite = - 7

hypotenuse = 5

cot x = - 24 / 7

adjacent / opposite = - 24 / 7

adjacent = 24

opposite = - 7

Identity : -

sec θ = hypotenuse / adjacent

hypotenuse² = 25

Similarly,

sec x = 25 / 24