Question

Given: In ∆ ,∠=°.

If 15 cot A=8, Find sin A

and sec A.​

Answer 1

Answer:

given

15 cotA = 8

cotA = 8/15

cot^2A = 64/225

cosec^2 A - 1 = 64/225

cosec^2A = 64/225 + 1

cosec^2A = 289/225

cosecA = 17/15 (taking positive value only)

1/sinA = 17/15

sinA = 15/17

sin^2 A = 225/289

1-cos2A = 225/289

cos^2A = 1-225/289

cos^2A = 64/289

cosA = 8/17 (taking positive value only)

secA = 17/8

(value of sinA and secA will be negative if A is in fourth quadrant)

Alternate method

cotA = 8/15 = [b/p] (angle A may be in first or fourth quadrant)

h = √b^2 + p^2

= √8^2 + 15^2

= √64 + 225

= √289

= 17

sinA = p/h = 15/17 (for fourth quadrant sinA = -15/17)

secA = [h/b] = 17/8 ( for fourth quadrant secA = -17/8)